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 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 roots are equal.
px2 – 4x + 3 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 0
Solve the following quadratic equation using formula method only
`3"x"^2 - 5"x" + 25/12 = 0 `
Find the value of k for which equation 4x2 + 8x – k = 0 has real roots.
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx2 + 6x - 3k = 0, k ≠ 0
Find whether the following equation have real roots. If real roots exist, find them.
8x2 + 2x – 3 = 0