Advertisements
Advertisements
Question
If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Advertisements
Solution
-5 is a root of the quadratic equation
2x2 + px – 15 = 0, then
⇒ 2(5)2 – p( -5) – 15 = 0
⇒ 50 – 5p – 15 = 0
⇒ 35 – 5p = 0
⇒ 5p = 35 = 0
⇒ p = `(35)/(5)` = 7
p(x2 + x) + k = 0 has equal roots
⇒ px2 + px + k = 0
⇒ 7x2 + 7x + k = 0
Here, a = 7, b = 7, c = k
b2 - 4ac
= (7)2 - 4 x 7 x k
= 49 - 28k
∵ Roots are equal
∴ b2 - 4ac = 0
⇒ 49 - 28k = 0
⇒ 28k = 49
⇒ k = `(49)/(28) = (7)/(4)`
∴ k = `(7)/(4)`.
APPEARS IN
RELATED QUESTIONS
Find the values of k for which the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 has equal roots. Also find these roots.
Determine the nature of the roots of the following quadratic equation:
`3x^2-2sqrt6x+2=0`
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
x2 + 4x + 5 = 0
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
Discuss the nature of the roots of the following equation: `sqrt(3)x^2 - 2x - sqrt(3)` = 0
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
