Question

If 1/2 is a root of the equation x2 + kx – 3= 0, then the value of k is
(A) #3(B) – 3 (C) 7 (D) -7

NCERT Class X
Mathematics - Exemplar Problems
Chapter _QUADRATIC EQUATIONS

Answer 1

Hii ☺ !!



One root = 1/2


P ( x ) = x² + kx - 3 = 0


P(1/2) = (1/2)² + k × 1/2 - 3 = 0



=> 1/4 + k/2 -3 = 0


=> 1 + 2k - 12 = 0


=> 2k - 11 = 0


=> 2k = 11

=> k = 11/2

Answer 2

❤❤Hello!!❤❤


Given equation

$x {}^{2} + kx - 3 = 0$

Given that 1 / 2 is a root of the given quadratic equation


Substitute x = 1 / 2

$= > ( \frac{1}{2} ) {}^{2} + k( \frac{1}{2} ) - 3 = 0 \\ \\ = > \frac{1}{4} + \frac{1}{2} k - 3 = 0 \\ \\ = > \frac{1}{4} - 3 + \frac{1}{2} k = 0 \\ \\ = > \frac{1 - 12}{4} + \frac{1}{2} k = 0 \\ \\ = > \frac{ - 11}{4} + \frac{1}{2} k = 0 \\ \\ = > \frac{1}{2} k = \frac{11}{4} \\ \\ = > k = \frac{11}{4} \times \frac{2}{1} \\ \\ = > k = \frac{11}{2} .$


Hence the value of k is 11 / 2.


Hope it helps!