Question

Find a quadratic polynomial, the sum and products of whoose zerores are 1/4 & -1 respectively

Answer 1

Answer:

4x^2 - x - 4

Step-by-step explanation:

Polynomial = kx^2 - (sum of zeroes)x + product of zeroes

= kx^2 - x/4 - 1

= 4x^2 - x - 4

Answer 2

$\huge{\underline{\underline{\pink{\mathcal{Solution}}}}}:-$

We know that,

Sum of Zereos = $\bold{ \alpha \; + \; \beta}$

Product of zereos = $\bold{\alpha \; \beta}$

If$\alpha$ and$\beta$ are zeroes of any quadratic polynomial then the quadratic equation can be written as :-

$\boxed {x^2 \;- \; \left( \alpha \; + \; \beta \right)\;x\; +\; \alpha\; \beta}$

Sum of zereos =$\frac{1}{4}$

Product of zereos = - 1

$\implies x^2 - \frac{1}{4} \; x \; +\; -1 \; = 0$

$\implies\bold{ 4x^2 \; - \; x \; - \;4}$

Thus, 4x² - x - 4 is the quadratic polynomial.

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