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Quadratic Equations

Question 1:

Find the nature of the roots of the following quadratic equations.

If the real roots exist, find them;

(I) 2x2 −3x + 5 = 0

(II)

(III) 2x2 − 6x + 3 = 0

Answer:

We know that for a quadratic equation ax2 + bx + c = 0, discriminant is b2 − 4ac.

(A) If b2 − 4ac > 0 → two distinct real roots

(B) If b2 − 4ac = 0 → two equal real roots

(C) If b2 − 4ac < 0 → no real roots

(I) 2x2 −3x + 5 = 0

Comparing this equation with ax2 + bx + c = 0, we obtain

a = 2, b = −3, c = 5

Discriminant = b2 − 4ac = (− 3)2 − 4 (…

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