Advertisements
Advertisements
Question
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
Solution
The equation `2x^2 - 6x + 9/2` = 0 has real and equal roots.
D = b2 – 4ac
= `(-6)^2 - 4(2)(9/2)`
= 36 – 36
= 0
Hence, the roots are real and equal.
APPEARS IN
RELATED QUESTIONS
For what value of m, are the roots of the equation (3m + 1)x2 + (11 + m) x + 9 = 0 equal?
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
Write the value of k for which the quadratic equation x2 − kx + 4 = 0 has equal roots.
Choose the correct answer from the given four options :
Which of the following equations has two distinct real roots?
Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
If b and c are odd integers, then the equation x2 + bx + c = 0 has ______.
