Question

if alpha and beta are zero of polynomial x^2 + 7x + 12 then form a quadratic polynomial whose zeroes are
$\alpha \: and \: 2 \beta$
Wrong answer will be reported.​

Answer 1

Apporpiate Question :-

If alpha and beta are zero of polynomial x^2 + 7x + 12 then form a quadratic polynomial whose zeroes are 2α and 2β

Given :-

Equation - x² + 7x + 12

To Find :-

Quadratic polynomial

Solution :-

On comparing with ax² + bx + c we get

a = 1

b = 7

c = 12

Sum of zeroes = -b/a

Sum = -(7)/1

Sum = -7/1

Sum = -7

Product of zeroes = c/a

Product =  12/1

Product = 12

Now, Quadratic polynomial whose zeroes are 2α and 2β

Sum of zeroes = 2α + 2β

Sum of zeroes = 2(α + β)

Sum of zeroes = 2(-7)

Sum of zeroes = -14

Product of zeroes = 2α × 2β

Product of zeroes = 4αβ

Product of zeroes = 4(12)

Product = 48

Now, Standard form of quadratic polynomial = x² - (α + β)x + αβ

Quadratic polynomial = x² - (-14) + 48

Quadratic polynomial = x² + 14x + 48