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Find the nature of the roots …

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Find the nature of the roots of the following quadratic equations. If the real roots exist find them: i)2x2-3x+5 ii)2x2-6x+3

Posted by Hemavardhini Madhu 4 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Yogita Ingle 4 years, 11 months ago

(i) 2x² – 3x + 5 = 0
Here, a = 2, b = -3, c = 5
b² – 4ac = (-3)²– 4(2) (5
= 9 – 40 = -31
b²– 4ac = -31 < 0
It has no real roots.

(iii) 2x² – 6x + 3 = 0

Here, a = 2, b = -6, c = 3

b² – 4ac = (-6)² – 4(2)(3) = 36 – 24 = 12

∴ b²– 4ac = 12 > 0.

∴ It has two distinct roots. 2x²– 6x + 3 = 0 Here, a = 2, b = -3, c = 3

0Thank You

Hemavardhini Madhu 4 years, 11 months ago

i) Consider the equation, 2x2-3x+5=0 Comparing with it ax2+bx+c=0 We get, a=2,b=-3,c=5 Discriminant(D)=b2-4ac =(-3)2-(4)(2)(5) =9-40 =-31 Since,D<0 No real roots is possible for the given equation.

1Thank You

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