Advertisements
Advertisements
Question
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
Options
`-1/2`
`1/2`
3
2
Advertisements
Solution
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is `underlinebb(1/2)`.
Explanation:
Given that,
`\implies` x = 3 is root of the quadratic equation
x2 – 2kx – 6 = 0
On putting x = 3 in the given equation,
`\implies` (3)2 – 2(k)(3) – 6 = 0
`\implies` 9 – 6k – 6 = 0
`\implies` 6k = 3
`\implies` k = `3/6 = 1/2`
APPEARS IN
RELATED QUESTIONS
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.
Without solving, examine the nature of roots of the equation 2x2 – 7x + 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
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and -ax2 + bx + c = 0 has real roots.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
The roots of the quadratic equation `2"x"^2 - 2sqrt2"x" + 1 = 0` are:
α and β are the roots of 4x2 + 3x + 7 = 0, then the value of `1/α + 1/β` is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 0
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
