Question

14)Find quadratic polynomial whose
sum is (-1/5) and product is (1/5)?
*
Vour answer​

Answer 1

Answer:5x^2+x+1

Step-by-step explanation:

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Answer 2

Given:

• Sum of zeroes = $- \frac{1}{5}$
• Product of zeroes = $\frac{1}{5}$

To find:

• The quadratic polynomial

Solution:

We know that,

Sum of zeroes = $- \frac{1}{5}$

Product of zeroes = $\frac{1}{5}$

And the Required Polynomial is given by

x²-(sum of zeroes)x + product of zeroes

Substituting values

${x}^{2} - \left ( - \frac{1}{5} \right) x+ \frac{1}{5} \\ \\ {x}^{2} + \frac{1}{5}x + \frac{1}{5} \\ \\ \text{Taking \: LCM} \\ \\ \frac{5 {x}^{2} + x + 1}{5}$

Let k be constant term

$\frac{k}{5} \left ( {5x}^{2} + x + 1 \right)\\ \\ \boxed{\green{5x^{2}+x+1}}$

Hence, the required polynomial is 5x² + x +1