Question

find a quadratic polynomial each with given number of sum and product of zeroes respectivel -1/4.1/4
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Answer 1

Hey Mate!!

Given ; i) Sum of zeroes = -1/4 ($\alpha + \beta )$

ii) Product of zeroes = 1/4($\alpha \times \beta)$

Now ;

$x^{2} - [ \alpha + \beta ] \times x + [\alpha \times \beta ]$

= ${x}^{2} - [\frac{ - 1}{4} ] \times x+ \frac{1}{4}$

= ${x}^{2} + \frac{1}{4}x + \frac{1}{4}$

Hence formed a Quadratic polynomial using α + β = -1/4 and α×β = 1/4 which is equal to ${x}^{2} + \frac{1}{4}x + \frac{1}{4}$

Hope this helps you!!