# Quadratic Equations

#### Question 1:

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

If the real roots exist, find them;

(I) 2*x*^{2
}−3*x *+ 5 = 0

(II)

(III) 2*x*^{2
}− 6*x *+ 3 = 0

#### Answer:

We know
that for a quadratic equation *ax*^{2 }+ *bx *+ *c*
= 0, discriminant is *b*^{2 }− 4*ac.*

(A) If *b*^{2
}− 4*ac* > 0 →
two distinct real roots

(B) If *b*^{2
}− 4*ac* = 0 →
two equal real roots

(C) If *b*^{2
}− 4*ac* < 0 →
no real roots

(I) 2*x*^{2
}−3*x *+ 5 = 0

Comparing this equation with *ax*^{2 }+ *bx *+ *c*
= 0, we obtain

*a* = 2, *b* = −3, *c* = 5

Discriminant = *b*^{2 }− 4*ac *= (− 3)^{2
}− 4...

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