Advertisements
Advertisements
Question
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Solution
`x^2 - 2sqrt(3)x - 1` = 0
Here `a = 1, b = -2sqrt(3), c = -1`
∴ D = b2 - 4ac
= `(-2sqrt(3))^2 - 4 xx 1 xx (-1)`
= 12 + 4
= 16
∴ D > 0
∴ Roots are real and unequal.
APPEARS IN
RELATED QUESTIONS
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
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:
(2k + 1)x2 + 2(k + 3)x + (k + 5) = 0
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: x2 + (p – 3)x + p = 0.
Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.
If one root of the quadratic equation 2x2 + kx – 6 = 0 is 2, the value of k is:
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.
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
