Exercise 4.3 Q2. CBSE 10th Maths NCERT exercise solution

Question: Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula:

i. 2x2 - 7x + 3 = 0
ii. 2x2 + x – 4 = 0
iii. 4x2+ 4$$sqrt3$x + 3 = 0 iv. 2x2 + x + 4 = 0 Video Explanation Explanatory Answer i. 2x2 - 7x + 3 = 0 The roots of ax2 + bx + c = 0 are $\frac {-b \pm \sqrt {{b}^{2}-4ac}} {2a}$ In this question a = 2, b = -7, c = 3 So, b2 – 4ac =$-7)2 – 4 * 2 * 3
= 49 - 24 = 25 > 0
∴ x = $$frac{-1{\pm }{\sqrt{33}}}{2*2}$ = $\frac{-1{\pm }{\sqrt{33}}}{4}$ x = $\frac{-1+{\sqrt33}}{4}$ and $\frac{-1-{\sqrt33}}{4}$ iii. 4x2 + 4√3 x + 3 = 0 The roots of ax2 + bx + c = 0 are $\frac {-b\pm \sqrt {{b}^{2}-4ac}} {2a}$ In this question a = 4, b = 4 √3 and c = 3 b2 – 4ac =$4 √3)2 - 4 * 4 * 3
= 48 - 48 = 0, which is not negative
∴ x = $$frac{-4{\sqrt3}{\pm } 0}{2 * 4}$ = -$\frac{\sqrt3}{2}$ and -$\frac{\sqrt3}{2}$ iv. 2x2 + x + 4 = 0 The roots of ax2 + bx + c = 0 are $\frac {-b\pm \sqrt {{b}^{2}-4ac}} {2a}$ In this question a = 2, b = 1 and c = 4 b2 – 4ac =$1)2 - 4 * 2 * 4 = 1 - 32 = - 31 < 0
Square root of a negative number is not real.
Hence, this equation does not have real roots.