true
(x + 5) (x + 1) = 0x2 + 6x + 5 = 0
Putting a negative number in parentheses merely assists a subtraction sum involving negative numbers. For example, 14 - (-17) = 31.
Two numbers are negative reciprocals if their product is -1. The numbers 1/2 and -2 are negative reciprocals. Their product is -1. This is often seen in problems involving the slopes of two lines. The slopes of perpendicular lines are negative reciprocals. Their product is -1.
The discriminant is the expression inside the square root of the quadratic formula. For a quadratic ax² + bx + c = 0, the quadratic formula is x = (-b +- Sqrt(b² - 4ac))/(2a). The expression (b² - 4ac) is the discriminant. This can tell a lot about the type of roots. First, if the discriminant is a negative number, then it will have two complex roots. Because you have a real number plus sqrt(negative) and real number minus sqrt(negative). You asked about irrational. If the discrimiant is a perfect square number {like 1, 4, 9, 16, etc.} then the quadratic will have two distinct rational roots (which are real numbers). If the discriminant is zero, then you will have a double root, which is a real rational number. So if the discrimiant is positive, but not a perfect square, then the roots will be irrational real numbers. If the discriminant is a negative number which is not the negative of a perfect square, then imaginary portion of the complex number will be irrational.
No, the range of a quadratic function is not all real numbers. A quadratic function, typically in the form ( f(x) = ax^2 + bx + c ), has a parabolic shape. If the coefficient ( a ) is positive, the range is all real numbers greater than or equal to the minimum point (the vertex), while if ( a ) is negative, the range is all real numbers less than or equal to the maximum point. Thus, the range is limited to values above or below a certain point, depending on the direction of the parabola.
The numbers can have a positive or negative sign.
imaginary numbers occur in the quadratic formula because of the radical symbol, and the possibility of a negative radican and that results in imaginary numbers. I hope this helped!
calculate long polynomials to high precision by the "method of differences", a technique resembling numerical integration but just involving enormous numbers of additions.
yes . .its all polynomials numbers only would be written in signed nos. .
(x + 5) (x + 1) = 0x2 + 6x + 5 = 0
Yes, it cannot contain any imaginary numbers
no
Putting a negative number in parentheses merely assists a subtraction sum involving negative numbers. For example, 14 - (-17) = 31.
Two numbers are negative reciprocals if their product is -1. The numbers 1/2 and -2 are negative reciprocals. Their product is -1. This is often seen in problems involving the slopes of two lines. The slopes of perpendicular lines are negative reciprocals. Their product is -1.
There is no specific term for such polynomials. They may be referred to as are polynomials with only purely complex roots.
there are none. you need to do the quadratic formula: X = -B + or - The Square Root of (B2 - 4xAC) 2xA
A rational number is able to be represented as a ratio of polynomials. pi/e is a ratio of irrational numbers, neither of which can be represented as a ratio of polynomials, and so I would conclude that pi/e is not rational. But it's a good question, because what if two irrational numbers could cancel out their irrationality, like two negative numbers! A quotient of two irrational numbers can be a rational number. Trivial example 2pi/pi = 2.