English

If one of the roots of quadratic equation x2 – kx – 15 = 0 is – 3, then find the value of ‘k’ - Algebra

Advertisements
Advertisements

Question

If one of the roots of quadratic equation x2 – kx – 15 = 0 is – 3, then find the value of ‘k’

Sum

Solution

– 3 is one of the roots of the equation x2 – kx – 15 = 0.

Putting x = – 3 in the given equation, we get

(– 3)2 – k(– 3) – 15 = 0

∴ 9 + 3k – 15 = 0

∴ 3k – 6 = 0

∴ 3k = 6

∴ k = `6/3`

∴ k = 2

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Quadratic Equations - Q.2 (B)

RELATED QUESTIONS

Solve : 7y = -3y2 - 4 


If the roots of x² + kx + k = 0 are real and equal, what is the value of k?


If α and β are the roots of the quadratic equation `x^2 - 4x - 6 = 0`, find  the values of (i) `α^2+β^2` (ii) `α^3+β^3`

 


Form the quadratic equation if the roots are 3 and 8.


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. 


Convert the following equations into simultaneous equations and solve:

`sqrt("x"/"y") = 4, 1/"x" + 1/"y" = 1/"xy"`


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?


Write the roots of following quadratic equation.

(p – 5) (p + 3) = 0


If one of the roots of quadratic equation x2 + kx + 54 = 0 is – 6, then complete the following activity to find the value of ‘k’.

Activity: One of the roots of the quadratic equation x2 + kx + 54 = 0 is – 6.

Therefore let’s take x = ______

(– 6)2 + k(– 6) + 54 = 0

(______) – 6k + 54 = 0

– 6k + ______ = 0

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 the roots of a quadratic equation are 4 and – 5, then form the quadratic equation


Solve the following quadratic equations by formula method.

5m2 – 4m – 2 = 0


Sum of the roots of the quadratic equation is 5 and sum of their cubes is 35, then find the quadratic equation


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 sum of the roots of the quadratic equation x2 + kx + 6 = 0 is 6, then the value of k is ______.


If the roots of the quadratic equation x2 + 12x + a = 0 are real and equal, then find the value of a.


The value of the discriminant of the equation x2 + 6x – 15 = 0 is ______.


If x = `sqrt(7) - 2`, find the value of `(x + 1/x)`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×