Advertisements
Advertisements
Question
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0
Advertisements
Solution
`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
RELATED QUESTIONS
Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
Find the values of k for which the roots are real and equal in each of the following equation:
k2x2 - 2(2k - 1)x + 4 = 0
If the roots of the equation (b − c) x2 + (c − a) x + (a − b) = 0 are equal, then prove that 2b = a + c.
Find the value of the discriminant in the following quadratic equation:
x2 +2x-2=0
Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0
The quadratic equation whose one rational root is `3 + sqrt2` is
Which of the following equations has two distinct real roots?
Solve the equation: 3x2 – 8x – 1 = 0 for x.
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.
