Question

If alpha,ß are zeroes are zeroes of the polynomial p(x)=x^2-(k-6)x+(2k+1) then find k. if alpha +beta= alpha x beta ​

Answer 1

$\Huge{\color{magenta}{\fbox{\textsf{\textbf{Question:-}}}}}$

If alpha,ß are zeroes are zeroes of the polynomial p(x)=x^2-(k-6)x+(2k+1) then find k. if alpha +beta= alpha x beta

$\Huge{\color{magenta}{\fbox{\textsf{\textbf{Answer:-}}}}}$

• α,β are the zeroes of x2−(k+6)x+2(2k−1)

i.e, α+β=k+6       ( Sum of roots of quadratic )

and αβ=2(2k−1)    ( Product of roots )

According to question, α+β=21αβ

⇒k+6=22(2k−1)=2k−1

⇒k+6=2k−1

⇒k=7

Hence, the answer is 7.

Answer 2

$\huge\mathfrak\pink{Answer}$

α,β are the zeroes of x2−(k+6)x+2(2k−1)

i.e, α+β=k+6 ( Sum of roots of quadratic )

and αβ=2(2k−1) ( Product of roots )

According to question, α+β=21αβ

⇒k+6=22(2k−1)=2k−1

⇒k+6=2k−1

⇒k=7

Hence, the answer is 7.