Advertisements
Advertisements
प्रश्न
Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0
उत्तर
`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
संबंधित प्रश्न
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
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.
Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.
If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – y)(α – δ) is ______.
The roots of quadratic equation x2 – 1 = 0 are ______.
The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal. Prove that: 2q = p + r, that is, p, q and r are in A.P.
The roots of quadratic equation x(x + 8) + 12 = 0 are ______.
