Advertisements
Advertisements
Question
If one root of the quadratic, x2 - 7x + k = 0 is 4. then find the value of k.
Solution
x2 - 7x + k = 0 ( Given )
∵ 4 is the root of this quadratic equation.
∴ 4 will satisfy this equation.
∴ Put x = a
42 - 7( 4) + k = 0
∴ 16 - 28 + k = 0
-12 + k = 0
∴ k = 12
APPEARS IN
RELATED QUESTIONS
If the roots of 2x2 - 6x + k = 0 are real and equal, find k.
Solve : 7y = -3y2 - 4
If α and β are the roots of the quadratice equation x²- 2x - 7= 0, find the
value α² + β²
Form the quadratic equation if the roots are 3 and 8.
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.
If one of the roots of quadratic equation X2 – kX + 27 = 0 is 3, then find the value of ‘k’
To decide whether 1 is a root of quadratic equation x2 + 4x – 5 = 0 or not, complete the following activity.
Activity: When x = (______)
L.H.S. = 12 + 4(______) – 5
= 1 + 4 – 5
= (______) – 5
= ______
= R.H.S
Therefore x = 1 is a root of quadratic equation x2 + 4x – 5 = 0
If one of the roots of quadratic equation x2 – kx – 15 = 0 is – 3, then find the value of ‘k’
If the roots of a quadratic equation are 4 and – 5, then form the quadratic equation
Roots of a quadratic equation are 5 and – 4, then form the quadratic equation
One of the roots of equation kx2 – 10x + 3 = 0 is 3. Complete the following activity to find the value of k.
Activity:
One of the roots of equation kx2 – 10x + 3 = 0 is 3.
Putting x = `square` in the above equation
∴ `"k"(square)^2 - 10 xx square + 3` = 0
∴ `square` – 30 + 3 = 0
∴ 9k = `square`
∴ k = `square`
Show that (x + 1) is a factor of the polynomial `x^3 - x^2 - (2 + sqrt(2))x + sqrt(2)`.
If x = `sqrt(7) - 2`, find the value of `(x + 1/x)`.
If 3 is one of the roots of the quadratic equation kx2 − 7x + 12 = 0, then k = ______.
