Find the roots of the quadratic equations :
(i) 5x2 + 13x + 2 = 0 (ii) 14x
2 + 9x + 1= 0
(iii) x2 + 4√3 x + 12 = 0 (iv) 3√2x2 – 5x – √2 = 0
class 10 quadratic equations
Answers
Let p(x) = x2 + 6x – 4,
It’s clearly seen that p(x) = x2 + 6x – 4 is a quadratic polynomial. Thus, the given equation is a quadratic equation.
(ii) √3x2 – 2x + 1/2 = 0
Solution:
Let p(x) = √3x2 – 2x + 1/2,
It’s clearly seen that p(x) = √3x2 – 2x + 1/2 having real coefficients is a quadratic polynomial. Thus, the given equation is a quadratic equation.
(iii) x2 + 1/x2 = 5
Solution:
Given,
x2 + 1/x2 = 5
On multiplying by x2 on both sides we have,
x4 + 1 = 5x2
⇒ x4 – 5x2 + 1 = 0
It’s clearly seen that x4 – 5x2 + 1 is not a quadratic polynomial as its degree is 4. Thus, the given equation is not a quadratic equation.
(iv) x – 3/x = x2
Solution:
Here, a= 3, b= – 4√3, c= 4
D = (- 4√3)2 -4(3)(4)
= 48 – 48
= 0
It’s seen that D = 0 and hence, the given equation has only 1 real and equal root.
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