Advertisements
Advertisements
Question
If 3 is one of the roots of the quadratic equation kx2 − 7x + 12 = 0, then k = ______.
Options
1
−1
3
−3
Solution
If 3 is one of the roots of the quadratic equation kx2 − 7x + 12 = 0, then k = 1.
Explanation:
The given quadratic equation is kx2 − 7x + 12 = 0
∴ Put x = 3
∴ k(3)2 − 7(3) + 12 = 0
∴ 9k − 21 + 12 = 0
∴ 9k − 9 = 0
∴ 9k = 9
∴ k = `9/9`
∴ k = 1
APPEARS IN
RELATED QUESTIONS
If one root of the quadratic, x2 - 7x + k = 0 is 4. then find the value of k.
Form the quadratic equation if its roots are 5 and 7.
Choose the correct alternative answer for the following sub-questions and write the correct alphabet.
Which of the following quadratic equation has roots – 3 and – 5?
Roots of a quadratic equation are 5 and – 4, then form the quadratic equation
If the roots of the given quadratic equation are real and equal, then find the value of ‘k’
kx(x – 2) + 6 = 0
Solve the following quadratic equation.
`sqrt(3) x^2 + sqrt(2)x - 2sqrt(3)` = 0
Solve the following quadratic equations by formula method.
5m2 – 4m – 2 = 0
Determine whether (x – 3) is a factor of polynomial x3 – 19x + 30.
Let P(x) = x3 – 19x + 30
By remainder theorem, `square` will be a factor of P(x), if P(3) = 0
Now, P(3) = `square` – 19 `square` + 30
= `square – square` + 30
= `square – square`
= 0
∵ P(3) = 0
Hence, `square` is a factor of polynomial x3 – 19x + 30.
If the roots of the quadratic equation x2 + 12x + a = 0 are real and equal, then find the value of a.
Is (x – 5) a factor of the polynomial x3 – 5x – 30?
