Advertisements
Advertisements
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
Advertisements
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.
APPEARS IN
RELATED QUESTIONS
Find the values of k for the following quadratic equation, so that they have two equal roots.
2x2 + kx + 3 = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
If a is a root of the equation x2 – (a + b)x + k = 0, find the value of k.
Find the discriminant of the following equations and hence find the nature of roots: 2x2– 3x + 5 = 0
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
If x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 0 has no real roots, then:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
The value of 'a' for which the sum of the squares of the roots of 2x2 – 2(a – 2)x – a – 1 = 0 is least is ______.
