Question

22. Find a quadratic polynomial, the sum and product of whose zeroes are
and -1
respectively.
​

Answer 1

Answer:

your question is not complete at all.

but I will gave the steps which can help you.

Step-by-step explanation:

• first the general form of a quadratic polynomial according to roots
• $\alpha \: and \: \beta$
• ${x}^{2} - ( \alpha + \beta )x + \alpha \beta$
• now you only given the value of product so ,
• $\alpha \beta = - 1$
• so the polynomial is :
• ${x }^{2} - ( \alpha + \beta )x - 1$
• thank u
• please mark as brainliest

Answer 2

$question :$

find a quadratic polynomial, the sum of whosi zeroes are 1/4 & -1

$answer : 4x {}^{2} - x - 4$

$solution :$

$let \: \alpha \: and \: \beta \: zeroes \: of \: quadratic \\ equation \\ a {x}^{2} + bx + c \\ given : \\ sum \: of \: zeroes \: \alpha + \beta = \frac{ - b}{a} = \frac{1}{4} \\ product \: of \: zeroes \: \alpha \beta = \frac{c}{d} = - 1 \\ if \: a = k \: where \: k \: is \: a \: real \: number \: \\ then \: form \: (1)and(2) \: we \: have \: \\ \\ b = \frac{ - k}{4} and \: c = - k \\ thus \\ quadratic \: polynomial \\ a {x}^{2} + bx + c \: is \\ obtained \: in \: the \: following \: form \\ : k {x}^{2} - \frac{k}{4} x - k \: or \: \frac{k}{4} (4 {x}^{2} - x - 4) \\ hence \\ = > required \: quadratic \: polynomial \: will \: \\ be \: : 4 {x}^{2} - x - 4$