Question

Find quadratic polynomial if their zeros are 1\4 and -1

Answer 1

lets a = 1/4 and b = -1

so a + b = 1/4 + (-1) = 1/4 - 1

= -3/4

ab = 1/4 × -1 = -1/4

Quadratic eq. is given by

$x {}^{2} - (a + b)x + ab = 0$

On putting values

$x {}^{2} - ( - 3 \div 4)x + ( - 1 \div 4) = 0$

x^2 +3/4x - 1/4 = 0

Multiply eq by 4

$4x {}^{2} + 3x - 1 = 0$


Thanks

Answer 2

Hiii friend,

(1/4) and -1 are the zero of the polynomial.

Let alpha = 1/4

and,

Beta = -1

Sum of zeros = (Alpha + Beta) = {1/4+(-1)} =1/4-1 = 1 - 4 = -3/4

Product of zeros = (Alpha × Beta) = 1/4 × -1 = -1/4

Therefore,

QUADRATIC POLYNOMIAL = X²-(Alpha+Beta)X + Alpha × Beta

=> X²-(-3/4)X+(-1/4)

=> X²+3X/4 + -1/4

=> X²+3X-1

Hence,

Quadratic polynomial = 4X²+3X-1

HOPE IT WILL HELP YOU...... :-)