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Q: What is the sum and product of roots of a quadratic equation?

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-4,3 are the roots of this equation, so for the values for which the sum of roots is 1 & product is -12

A quadratic equation has the form: x^2 - (sum of the roots)x + product of the roots = 0 or, x^2 - (r1 + r2)x + (r1)(r2) = 0

b is the negative sum of the roots of the equation

-9

It has no roots because the discriminant of the given quadratic equation is less than zero.

This quadratic equation has no real roots because its discriminant is less than zero.

Sum

A product is the answer of a multiplication equation. A sum is the answer of an addition equation.

find the sum and product of the roots of 8×2+4×+5=0

19

x2 + 15x +36

A quadratic equation has the form: x^2 - (sum of the roots)x + (product of the roots) = 0 If the roots are imaginary roots, these roots are complex number a+bi and its conjugate a - bi, where a is the real part and b is the imaginary part of the complex number. Their sum is: a + bi + a - bi = 2a Their product is: (a + bi)(a - bi) = a^2 + b^2 Thus the equation will be in the form: x^2 - 2a(x) + a^2 + b^2 = 0 or, x^2 - 2(real part)x + [(real part)^2 + (imaginary part)^2]= 0 For example if the roots are 3 + 5i and 3 - 5i, the equation will be: x^2 - 2(3)x + 3^2 + 5^2 = 0 x^2 - 6x + 34 = 0 where, a = 1, b = -6, and c = 34. Look at the denominator of this quadratic equation: D = b^2 - 4ac. D = (-6)^2 - (4)(1)(34) = 36 - 136 = -100 D < 0 Since D < 0 this equation has two imaginary roots.

You can solve a quadratic equation 4 different ways. graphing, which is quick but not reliable, factoring, completing the square and using the quadratic formula. There is a new fifth method, called Diagonal Sum Method, that can quickly and directly give the 2 roots in the form of 2 fractions, without having to factor the equation. It is fast, convenient, and is applicable whenever the equation can be factored. Finally, you can proceed solving in 2 steps any given quadratic equation in standard form. If a=1, solving the equation is much simpler. First, you always solve the equation in standard form by using the Diagonal Sum Method. If it fails to find answer, then you can positively conclude that the equation is not factorable, and consequently, the quadratic formula must be used. In the second step, solve the equation by using the quadratic formula.

parallel

If the given information is the sum and the product of two numbers, then the numbers are not integers, because only 1*21 or 3*7 equals 21, and their sum is different from 27. So let's write the quadratic form of an equation given the sum and the product of roots, and solve it. The sum = 27, the product = 21 x2 - (summ of the roots)x + (product of the roots) = 0 x2 - 27x + 21 = 0; a = 1, b = -27, and c = 21 x = [-b ± √(b2 - 4ac)]/(2a) the quadratic formula x ={-(-27) ± √[(-27)2 - 4(1)(21)]/[2(1)] = [27 ± √(729 - 84)]/2 = (27 ± √645)]/2 Thus, the numbers are (27 - √645)]/2 and (27 + √645)]/2.

(√x + √y) = 5√(xy) = -14(√x + √y) - 5= √(xy) + 14From Superscot85: You asked for a quadratic, the above isn't but this is:x2 - 5x - 14 = 0 ie (x - 7)(x + 2) = 0 and roots are 7 and -2.

There are no integer answers for your question. I suggest using the quadratic equation is is y=b±√b²-4(a*c)∕2*a

The numbers are 15.75 and -5.75 When tackling probiems like this form a quadratic equation with the information given and solving the equation will give the solutions.

Um, x2+3x-5=0? This is ax2+bx+c where a=1, b=3, and c=-5. The sum of the roots is -b/a so that means the sum of the roots is -3. Also, product of the roots is c/a. That means the product of the roots is -5. -3+(-5)= -8. There you have it.

If you have a quadratic, which is factored like (x - P)(x - Q) = 0, so P & Q are solutions for x. Multiplying the binomials gives: x2 - Px - Qx + PQ = 0 ---> x2 - (P+Q)x + PQ = 0, so the negative of the sum is the coefficient of the x term, and the product is the constant term (no variable x).

multiply by one if ur looking for the sum and divide by one if look ing for the product, easy

There is a new method, called Diagonal Sum Method, that quickly and directly give the 2 roots without having to factor the equation. The innovative concept of this method is finding 2 fractions knowing their sum (-b/a) and their product (c/a). It is fast, convenient and is applicable to any quadratic equation in standard form ax^2 + bx + c = 0, whenever it can be factored. If it fails to find answer, then the equation is not factorable, and consequently, the quadratic formula must be used. So, I advise you to proceed solving any quadratic equation in 2 steps. First, find out if the equation can be factored? How?. Use this new method to solve it. It usually takes fewer than 3 trials. If its fails then use the quadratic formula to solve it in the second step. See book titled:" New methods for solving quadratic equations and inequalities" (Trafford Publishing 2009)

In general, there are two steps in solving a given quadratic equation in standard form ax^2 + bx + c = 0. If a = 1, the process is much simpler. The first step is making sure that the equation can be factored? How? In general, it is hard to know in advance if a quadratic equation is factorable. I suggest that you use first the new Diagonal Sum Method to solve the equation. It is fast and convenient and can directly give the 2 roots in the form of 2 fractions. without having to factor the equation. If this method fails, then you can conclude that the equation is not factorable, and consequently, the quadratic formula must be used. See book titled:" New methods for solving quadratic equations and inequalities" (Trafford Publishing 2009) The second step is solving the equation by the quadratic formula. This book also introduces a new improved quadratic formula, that is easier to remember by relating the formula to the x-intercepts with the parabola graph of the quadratic function.

an + an = 2an; an x an = an + n

11 and 11. In general, you can write an equation (or two equations), and solve with the quadratic formula, to solve this type of questions.