Q. 84.5( 2 Votes )

# The nature of roots of the quadratic equation 4x^{2} – 12x – 9 = 0 is :

A. real and equal

B. real and distinct

C. imaginary and equal

D. imaginary and distinct

Answer :

The nature of roots of the equation can be found out using the following formula:

⟹ b^{2} – 4ac

When we compare the above quadratic equation with the generalized one we get,

ax^{2} + bx + c = 0

∴ a = 4

b = -12

c = -9

⟹ b^{2} – 4ac

⟹ (-12)^{2} – (4 × -9 × 4)

⟹ 144 – (-144)

⟹ 144 + 144

= 288

Since b^{2} – 4ac>0, the roots will be real and distinct.

So the correct answer is B [real and distinct].

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