Advertisements
Advertisements
Question
Write the value of k for which the quadratic equation x2 − kx + 4 = 0 has equal roots.
Advertisements
Solution
The given quadric equation is `x ^2 - kr + 4 = 0`, and roots are equal.
Then find the value of k.
Here, a = 1, b = -k and , c = 4
As we know that `D = b^2 - 4ac`
Putting the value of a =1,b = -k and , c = 4
=` (-k)^2 - 4 xx 1 xx 4`
=` k^2- 16`
The given equation will have equal roots, if D = 0
`k^2 - 16 = 0`
`k^2 = 16`
`k = sqrt 16`
=± 4
Therefore, the value of k =± 4 .
APPEARS IN
RELATED QUESTIONS
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 - 6x + 3 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 + kx + 9 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
9x2 - 24x + k = 0
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
`10x -(1)/x` = 3
ax2 + (4a2 - 3b)x - 12 ab = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 2x + 4 = 0
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Choose the correct answer from the given four options :
If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
What is the value of discriminant for the quadratic equation X2 – 2X – 3 = 0?
The quadratic equation whose one rational root is `3 + sqrt2` is
If (x – a) is one of the factors of the polynomial ax2 + bx + c, then one of the roots of ax2 + bx + c = 0 is:
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
Find whether the following equation have real roots. If real roots exist, find them.
8x2 + 2x – 3 = 0
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
