Advertisements
Advertisements
प्रश्न
Discuss the nature of the roots of the following equation: `sqrt(3)x^2 - 2x - sqrt(3)` = 0
उत्तर
`sqrt(3)x^2 - 2x - sqrt(3)` = 0
Here `a = sqrt(3), b = -2, c = -sqrt(3)`
∴ D = b2 - 4ac
= `(-2)^2 - 4 xx sqrt(3) xx (-sqrt(3))`
= 4 + 12
= 16
∵ D > 0
∴ Roots are real and distinct.
APPEARS IN
संबंधित प्रश्न
Without solving, examine the nature of roots of the equation x2 – 5x – 2 = 0
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 3x + 5 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 3 = 0
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0
Choose the correct answer from the given four options :
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)
If a = 1, b = 4, c = – 5, then find the value of b2 – 4ac
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.
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
