Question

find a quadratic polynomial whose sum and product of zeros are 1 by 4 and -1​

Answer 1

Answer:

4x²-x-4

Step-by-step explanation:

given sum is 1/4

product is -1.

let roots be a,b.

general quadratic polynomial is k(x²-(a+b)x+ab)

k(x²-1/4x-1)

if k is 4.

then the quadratic polynomial is 4x²-x-4

Answer 2

$\underline{\boxed{\bold{Question}}}$  

↠  Find a quadratic polynomial whose sum and product of zeros are 1/4 and -1 respectively.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold{Important\;Information}}}$  

↠ Sum of roots = (-b)/a

↠ Product of roots = c/a

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold{Given}}}$

↠  Sum of roots = α + β = 1/4

↠ Product of roots = αβ = (-1)

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold{Answer}}}$

Let's Start !

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Every quadratic equation can be expressed in form given below.

$\underline{\boxed{x^{2} -(\alpha +\beta )x+\alpha \beta =0}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Now let's substitute values in the given equation.

$:\implies x^{2} -(\alpha +\beta )x+\alpha \beta =0$

$:\implies x^{2} -(\frac{1}{4} )x+(-1) =0$

$\boxed{:\implies 4x^{2} -x-1 =0}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\boxed{\boxed{\bold{\therefore Required\; Polynomial =( 4x^{2} -x-1 =0)}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Hope this helps u.../

【Brainly Advisor】