Question

8. Find a quadratic polynomial whose sum and product of its zeroes are 1 by 4
and -1 respectively​

Answer 1

Answer:

4x²+x-4

Step-by-step explanation:

Given that the sum of zeroes of a quadratic polynomial is 1/4

And product of zeroes of a quadratic polynomial is - 1

Sum of zeroes of a quadratic polynomial = 1/4

-b/a = 1/4

Product of zeroes of the quadratic polynomial = - 1

c/a = - 1 (since a is 1 in product side we need to multiply it with 4 because in the sum of zeroes a is 4 to balance the values)

So when we multiply with 4 we obtain c/a = - 4/4

So the values are a = 4 b = 1 c = - 4

Substitute in the standard form ax²+bx+c = 0

4x²+1x-4=0

Answer 2

Answer:

$Given, \: Sum \: of \: zeroes \: = 1/4</p><p> \\ and \: product \: of \: zeros = \: -1 \\ </p><p>Then, \: the \: quadratic \: polynomial \\ = k \: [ {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes ] \\ k( {x}^{2} - ( \frac{1}{4} )x - 1 \\ = k( {x}^{2} - \frac{x}{4} - 1) \\ = k( \frac{4 {x}^{2} - x - 4 }{4 } ) \\ If \: k = 4, \: then \: the \: required \: quadratic \: polynomial \: is \\⇒ \: 4 {x}^{2} - x - 4</p><p>$