Advertisements
Advertisements
Question
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
Advertisements
Solution
3x2 – 8x – (2k + 1) = 0
α = 7β ...(Given)
α + β = `- (-8)/3 = 8/3`
7β + β = `8/3`
`\implies` β = `1/3`
αβ = `(-(2k + 1))/3`
7ββ = `(-(2k + 1))/3`
`7 xx 1/9 = (-(2k + 1))/3`
7 = – 6k – 3
k = `10/(-6) = (-5)/3`
∴ k = `(-5)/3`
APPEARS IN
RELATED QUESTIONS
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Solve the following quadratic equation using formula method only
x2 - 4x - 1 = 0
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" = 3`
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
The quadratic equation whose roots are 1:
Solve for x: 9x2 – 6px + (p2 – q2) = 0
Which of the following equations has two real and distinct roots?
