Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 2(k + 1)x + (k + 4) = 0
Advertisements
उत्तर
The given quadric equation is 4x2 - 2(k + 1)x + (k + 4) = 0, and roots are real and equal
Then find the value of k.
Here,
a = 4, b = -2(k + 1) and c = k + 4
As we know that D = b2 - 4ac
Putting the value of a = 4, b = -2(k + 1) and c = k + 4
= {-2(k + 1)}2 - 4 x 4 x (k + 4)
= {4(k2 + 2k + 1)} - 16(k + 4)
= 4k2 + 8k + 4 - 16k - 64
= 4k2 - 8k - 60
The given equation will have real and equal roots, if D = 0
4k2 - 8k - 60 = 0
4(k2 - 2k - 15) = 0
k2 - 2k - 15 = 0
Now factorizing of the above equation
k2 - 2k - 15 = 0
k2 + 3k - 5k - 15 = 0
k(k + 3) - 5(k + 3) = 0
(k + 3)(k - 5) = 0
So, either
k + 3 = 0
k = -3
Or
k - 5 = 0
k = 5
Therefore, the value of k = -3, 5.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0
Without solving, examine the nature of roots of the equation 2x2 + 2x + 3 = 0
If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x2 + 5(p + q) x− 2(p − q) = 0 are real and unequal.
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Find the value of the discriminant in the following quadratic equation:
x2 +2x-2=0
Find the value of the discriminant in the following quadratic equation :
`4 sqrt 3 "x"^2 + 5"x" - 2 sqrt 3 = 0`
Determine the nature of the roots of the following quadratic equation :
4x2 - 8x + 5 = 0
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
48x² – 13x -1 = 0
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Solve for x: (x2 - 5x)2 - 7(x2 - 5x) + 6 = 0; x ∈ R.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are:
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
