Question

If alpha and beta are zeroes of quadratic polynomial x^2+x-2 then find a polynomial whose zeroes are 2a+1 and 2b+1?​

Answer 1

Answer:

you have to ask the question as the zeroes are a and b.

${x}^{2} + x - 2 = 0 \\ middile \: term \: splitting \\ {x}^{2} + 2x - x - 2 = 0 \\ x(x + 2) - 1(x + 2) = 0 \\ (x - 1)(x + 2) = 0 \\ x = 1 \: or \: x = - 2 \\ \alpha = 1 \: and \: \beta = - 2$

substituting these values

2(1)+1=3

2(-2)+1=-3

we know that the sum of zeroes =-b/a

3+(-3)=-b/a

0=b/a

product of zeroes =c/a

3(-3)=c/a

=-9/1

quadratic equation =

$a {x}^{2} + bx + c \\(1) {x}^{2} +( 0)x + ( - 9) \\ = {x}^{2} - 9$