Class ten Quadratic Equations NCERT Solutions
Chapter 4: Quadratic Equations
TEXTBOOK’S EXERCISE 4.3
1. Find the roots of the following quadratic equations, if they exist, by the method of completing the square :
(i) 2x2 – 7x + 3 = 0
(ii) 2x2 + x – 4 = 0
(iv) 2x2 + x + 4 = 0
Sol. (i) Given equation is : 2x2 – 7x + 3 = 0
⇒ 2x2 – 7x = –3
Dividing both sides by 2, we get
⇒ x = 2/4 =1/2
Hence, the roots of a quadratic equation are 12 and 3.
(ii) Given equation is : 2x2 + x – 4 = 0
⇒ 2x2 + x = 4
Dividing both sides by 2, we get
Adding (1/4) 2 to both sides, we get
Hence, the roots of a quadratic equation are
Hence, the roots of the given quadratic equation are
(iv) Given equation is : 2x2 + x + 4 = 0
⇒ 2x2 + x = – 4
Dividing both sides by 2, we get
Adding (1/4)2 to both sides, we get
Since the square of any number cannot be negative. So,
cannot be negative for any real x.
∴ There is no real x which satisfies the given quadratic equation. Hence, given the quadratic equation has no real roots.
2. Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.
Sol. (i) Given equation is : 2x2 – 7x + 3 = 0
This is of the form ax2 + bx + c = 0
Where a = 2, b = –7, c = 3
Now, b2 – 4ac = (–7)2 – 4 × 2 × 3 = 49 – 24 = 25
= 12/4 and 2/4 = 3 and 1/2
Hence, 3 and 1/2 are the roots of given quadratic equation.
(ii) Given equation is : 2x2 + x – 4 = 0
This is of the form ax2 + bx + c = 0.
Where a = 2, b = 1, c = – 4
Now, b2 – 4ac = (1)2 – 4 × 2 × (– 4) = 1 + 32 = 33
are the roots of given quadratic equation.
are the roots of given quadratic equation.
(iv) Given equation is : 2x2 + x + 4 = 0
This is of the form ax2 + bx + c = 0.
Where, a = 2, b = 1, c = 4
Now, b2 – 4ac = (1)2 – 4 × 2 × 4 = 1 – 32
= –31 < 0
As, b2 – 4ac < 0, therefore the given quadratic equation will have no real roots.