Question

If alpha and beta are the zeroes of the polynomial x2-6x+8 ,then form a quadratic polynomial whose zeroes are 1/2alpha and 1/2beta

Answer 1

this is the answer taht i solved and got...

Hope it helps!

Answer 2

$f(x) = x^2 -3x +2$

is the required polynomial.

Step-by-step explanation:

We are given the following polynomial:

$x^2-6x+8$

To find the zeroes of the polynomial:

$x^2-6x+8 = 0\\x^2-4x-2x+8 = 0\\x(x-4) - 2(x-4) = 0\\(x-4)(x-2) = 0\\x-4 = 0, x - 2 =0\\x = 4, x = 2\\\alpha = 4, \beta = 2$

New zeroes of polynomial:

$\alpha' = \dfrac{\alpha}{2},\beta' = \dfrac{\beta}{2}\\\\\alpha' = 2, \beta' = 1\\\alpha' + \beta' = 3\\\alpha'\beta' = 2$

New polynomial:

$x^2-(\alpha' + \beta')x + \alpha'\beta'\\f(x) = x^2 -3x +2$

is the required polynomial.

#LearnMore

If alpha and beta are zeroes of the quadratic polynomial f(x) = x2+x-2 then find a polynomial whose zeroes are 2alpha + 1 and 2beta + 1​

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