Advertisements
Advertisements
प्रश्न
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
Advertisements
उत्तर
(4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0
Here a = (4 – k), b = 2 (k + 2), c = 8k + 1
∴ D = b2 – 4ac
= [2(k + 2)]2 – 4 x (4 – k)(8k + 1) = 0
= 4(k + 2)2 - 4(32k + 4 – 8k2 – k)
= 4(k2 + 4k + 4) –4(32k + 4 – 8k2 – k)
= 4k2 + 16k + 16 - 128k – 16 + 32k2 + 4k
= 36k2 – 108k
= 36k(k – 3)
∵ Roots are equal
∴ D = 0
⇒ 36k(k – 3) = 0
⇒ k(k – 3) = 0
Either k = 0
or
k – 3 = 0,
then k= 3
k = 0, 3.
APPEARS IN
संबंधित प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 3x + 5 = 0
Find the value of the discriminant in the following quadratic equation:
2x2 - 5x + 3 = 0
From the quadratic equation if the roots are 6 and 7.
ax2 + (4a2 - 3b)x - 12 ab = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 5 = 0
Find the values of k for which each of the following quadratic equation has equal roots: x2 – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.
Choose the correct answer from the given four options :
If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are
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
Which of the following equations has the sum of its roots as 3?
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 4)2 – 8x = 0
