Advertisements
Advertisements
प्रश्न
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
उत्तर
Given –5 is a root of the quadratic equation 2x2 + px – 15 = 0.
∴-5 satisfies the given equation.
∴ 2(5)2+ p(-5)-15 = 0
∴ 50 - 5p - 15= 0
∴ 35-5p = 0
∴5p = 35 ⇒ p = 7
Substituting p = 7 in p(x2 + x)+ k= 0,we get
7(x2+x)+k=0
∴7x2 + 7x + k = 0
The roots of the equation are equal.
∴ Discriminant b2 - 4ac = 0
Here, a=7, b=7, c=k
b2-4ac=0
∴ (7)2 - 4(7)(k)=0
∴ 49-28k= 0
∴28k = 49
∴ k = `49/28=7/4`
APPEARS IN
संबंधित प्रश्न
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
Find the value of the discriminant in the following quadratic equation:
2x2 - 5x + 3 = 0
Find the value of the discriminant in the following quadratic equation :
10 x - `1/x` = 3
Determine the nature of the roots of the following quadratic equation :
x2 -4x + 4=0
Determine the nature of the roots of the following quadratic equation :
4x2 - 8x + 5 = 0
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
If the difference of the roots of the equation x2 – bx + c = 0 is 1, then:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 0`
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
