# Frame Quadratic Equations | Find roots

Exercise 4.3 Q5. NCERT solutions for class 10 maths

#### Explanatory Answer

Step 1: Frame equations from the statements given in the question.
Let her marks in Math be M.
Let her marks in English be E.
Sum of the marks in Math and English is 30 = M + E = 30
∴ M = 30 - E ---------(1)
Had she got 2 more marks in Math, her marks in Math would be (M + 2) ---------(2)
Had she got 3 lesser in English, her marks in English would be (E - 3) ---------(3)
The product of (2) and (3) is 210
i.e., (M + 2) (E - 3) = 210
Substitute M as (30 - E) from (1)
(30 - E + 2)(E - 3) = 210
(32 - E)(E - 3) = 210
32E - 96 – E2 + 3E = 210
E2 – 35E + 306 = 0

##### Step 2: Find the roots either by factorizing or by using the quadratic formula

Method 1: Factorize the equation to find values of E.
E2 - 18E - 17E + 306 = 0
E(E – 18) – 17(E – 18) = 0
(E – 18) (E – 17) = 0
E = 18 and E = 17
If E = 18, M = 30 – E = 30 – 18 = 12
If E = 17, M = 30 – E = 30 – 17 = 13

Method 2: Use the quadratic formula to find values of E.
The roots of ax2 + bx + c = 0 are $$frac {-b\pm \sqrt {{b}^{2}-4ac}} {2a}$ In this equation, a = 1, b = -35 and c = 306 b2 – 4ac =$-35)2 – 4 * 1 * 306 = 1225 – 1224 = 1 > 0
Therefore, E = $$frac{-$-35$ 士 {$sqrt1}}{2}$ = $\frac{35 士 1}{2}$
E = 18 and E = 17.
Therefore, M = 12 and M = 13.