Advertisements
Advertisements
प्रश्न
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0
Advertisements
उत्तर
`3x^2 - 4sqrt(3)x + 4` = 0
Here a = 3, b = `-4sqrt(3)`, c = 4
∴ D = b2 - 4ac
= `(-4sqrt(3))^2 - 4 xx 3 xx 4`
= 48 - 48
= 0
∵ D = 0
∴ Roots are real and equal.
APPEARS IN
संबंधित प्रश्न
Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3
Find the value of k for which the roots of the equation 3x2 -10x +k = 0 are reciprocal of each other.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Find the value(s) of p for which the quadratic equation (2p + 1)x2 – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
Which of the following equations has the sum of its roots as 3?
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 0
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
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.
