Question

the quadratic polynomial, the sum and the product of whose zeros are -1/4 and 1/4 respectively- (a)4x²-x+1(b)4x+x+1 (c)x²-4x+4(d)x²+4x-1

Answer 1

Sum of zeroes, S = - 1/4

Product of zeroes, P = 1/4

The requires polynomial is –

$<b>f (x) = k [ x² - ( Sum of zeroes )x + ( Product of zeroes ) ]</b>$

f (x) = k [ x² - ( -1/4 )x + ( 1/4 ) ]

f (x) = k [ x² + 1/4 + 1/4 ]

f (x) = k [ ( 4x² + 1 + 1 ) / 4 ]

f (x) = k/4 ( 4x² + 1 + 1 )

Put k = 4

f (x) = 4x² + 1 + 1

$<b>Option (b)</b>$ is correct.

Answer 2

Step-by-step explanation:

Let a and b its roots

a+b=−4 and ab=−1

∴ The equation is x

2

−(a+b)x+ab=0

⇒x

2

+4x−1=0