Question

if alpha and beta are zeros of polynomial x square - 7 x + 10 then form a quadratic polynomial whose zeros are half the zeros of given polynomial​

Answer 1

Solution by RKRAUSHAN

HOPE It will help u

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Answer 2

$f(x) = x^2 -\dfrac{7}{2}x +\dfrac{5}{2}$

is the required polynomial.

Step-by-step explanation:

We are given the following polynomial:

$x^2 - 7x +10$

To find the zeroes of the polynomial:

$x^2-7x+10 = 0\\x^2-5x-2x+10 = 0\\x(x-5) - 2(x-5) = 0\\(x-5)(x-2) = 0\\x-5 = 0, x - 2 =0\\x = 5, x = 2\\\alpha = 5, \beta = 2$

New zeroes of polynomial:

$\alpha' = \dfrac{\alpha}{2},\beta' = \dfrac{\beta}{2}\\\\\alpha' = 2.5, \beta' = 1\\\alpha' + \beta' = 3.5 = \dfrac{7}{2}\\\alpha'\beta' = 2.5 = \dfrac{5}{2}$

New polynomial:

$x^2-(\alpha' + \beta')x + \alpha'\beta'\\\\f(x) = x^2 -\dfrac{7}{2}x +\dfrac{5}{2}$

is the required polynomial.

#LearnMore

If alpha and beta are the zeros of a quadratic polynomial f(x)=3x2-7x-6, find a polynomial whose zeros are :i) alpha2 and beta2, ii)2alpha+3beta and 3alpha +2beta

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