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Mathematics · Quadratic Equations · NCERT Examples

Example 9

A complete, independently verified solution for NCERT Example 9.

Mathematics · Chapter 4 · NCERT Examples

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NCERT Example

Example 9

discriminant · equal roots

Find the discriminant and roots of 3x2−2x+13=0.\text{Find the discriminant and roots of }3x^2-2x+\frac13=0.

Solution

a=3,b=−2,c=13a=3,\quad b=-2,\quad c=\frac13
D=(−2)2−4(3)(13)=0D=(-2)^2-4(3)\left(\frac13\right)=0
x=−b2a=26=13x=\frac{-b}{2a}=\frac{2}{6}=\frac13

D = 0, so this root is repeated; substitution in the original equation gives 0.

Final answer

x=13,13x=\frac13, \frac13