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∙ 14y agotrue
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∙ 14y ago(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.
Yes. But note that if b2 - 4ac is negative, there are no real solutions to the quadratic equation to be found. When complex numbers are used, this is not a problem as sqrt(-1) = i and so if b2 - 4ac is negative, "sqrt(b2 - 4ac)" becomes "i sqrt(4ac - b2)", meaning the solutions are: x = -b/2a + i/2a sqrt(4ac-b2) x = -b/2a - i/2a sqrt(4ac-b2)
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.
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.
there are none. you need to do the quadratic formula: X = -B + or - The Square Root of (B2 - 4xAC) 2xA