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प्रश्न
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 0
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उत्तर
The equation 2x2 + x – 1 = 0 has two real and distinct roots.
D = b2 – 4ac
= 12 – 4(2)(–1)
= 1 + 8 > 0
Hence, the roots are real and distinct.
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Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
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