Advertisements
Advertisements
Question
Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0
Advertisements
Solution
`2sqrt(3)x^2 - 5x + sqrt(3)` = 0
Here `a = 2sqrt(3), b = -5, c = sqrt(3)`
∴ D = b2 - 4ac
= `(-5)^2 - 4 xx 2sqrt(3) xx sqrt(3)`
= 25 - 24
= 1
∵ D > 0
∴ Roots are real and distinct.
APPEARS IN
RELATED QUESTIONS
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
Find the value of the discriminant in the following quadratic equation:
2x2 - 3x + 1 = O
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.
In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p2 – q2)x2 – (q2 – r2)x + (r2 – p2) = 0 are:
If x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 0 has no real roots, then:
If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
Which of the following equations has imaginary roots?
One root of equation 3x2 – mx + 4 = 0 is 1, the value of m is ______.
