Question

write a quadretic polynomials, sun of whose zeroes is 1\4 and product is -1​

Answer 1

Given :

• sum of zeroes = ¼
• product of zeroes = -1

To Find :

• quadratic polynomial ?

Solution :

we know that,

$\bold{sum \: of \: zeroes = \frac{ - coefficient \: of \: x }{cefficient \: of \: {x}^{2} } }$

and

$\bold{product \: of \: zeroes = \frac{constant \: term}{coefficient \: of \: {x}^{2} } }$

if a and b are sum and product of zeroes respectively then,

$\boxed{ \red{\bold{p(x) = {x}^{2} - ax + b}}}$

here,

• a = ¼
• b = -1

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

so, the quadratic polynomial p(x) = 4x² - x - 4