Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
kx(x - 2) + 6 = 0
उत्तर
The given equation is
kx(x - 2) + 6 = 0
⇒ kx2 - 2kx + 6 = 0
The given equation is in the form of ax2 + bx + c = 0
where a = k, b = -2k and c = 6
Therefore, the discriminant
D = b2 - 4ac
= (-2k)2 - 4 x (k) x (6)
= 4k2 - 24k
= 4k(k - 6)
∵ Roots of the given equation are real and equal
∴ D = 0
⇒ 4k(k - 6) = 0
⇒ k = 0
Or
⇒ k - 6 = 0
⇒ k = 6
Hence, the value of k = 0, 6.
APPEARS IN
संबंधित प्रश्न
Find the values of k for the following quadratic equation, so that they have two equal roots.
kx (x - 2) + 6 = 0
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
In each of the following, determine whether the given numbers are roots of the given equations or not; 6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
If one root of the equation x2+ px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, the value of q is:
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
