Question

If alpha and beta are zeros of polynomial 21x2-x-2 find the quadratic polynomial whose zeros are 2alpha and 2beta

Answer 1

Here is your answer user.

Answer 2

Concept

In algebra, a quadratic equation is any equation that has the power 2 or more. For example x²-8x-3 = 0

Given

1) a and b are the zeroes of equation 21x²-x-2 = 0

Find

The quadratic equation whose zeroes are 2a and 2b

Solution

Solving equation

21x²-x-2 = 0

21x²-7x + 6x -2 = 0

7x(3x-1) + 2(3x-1) = 0

(7x+2)(3x-1) = 0

x = -2/7 or 1/3

Let a = 1/3 and b = -2/7

Zeroes of new quadratic equation are

a' = 2a = 2(1/3) = 2/3

b' = 2b = -4/7

Equation of quadratic equation with zeroes a' and b'

(x-a')(x-b') = 0

(x-2/3)(x+4/7) = 0
(3x-2)(7x+4)

21x² -14x+12x -8 = 0

21x²-2x-8 = 0

The quadratic polynomial whose zeros are 2a and 2b is 21x²-2x-8 = 0

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