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Question
Choose the correct answer from the given four options :
Which of the following equations has two distinct real roots?
Options
`2x^2 - 3sqrt(2)x + (9)/(4)` = 0
x² + x – 5 = 0
`x^2 + 3x + 2sqrt(2)` = 0
5x² – 3x + 1 = 0
Solution
`2x^2 - 3sqrt(2)x + (9)/(4)` = 0
b2 - 4ac
= `(-3sqrt(2))^2 - 4 xx 2 xx (9)/(4)`
= 18 - 18
= 0
∴ Roots are real and equal.
x² + x – 5 = 0
b2 - 4ac
= (1)2 - 4 x 1 x (-5)
= 1 + 20
= `sqrt(21)` > 0
∴ Roots are real and distinct.
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