English

If -2 is a Zero of the Polynomial `3x^2 + 4x + 2k` Then Find the Value of K. - Mathematics

Advertisements
Advertisements

Question

If -2 is a zero of the polynomial `3x^2 + 4x + 2k` then find the value of k. 

 

Advertisements

Solution

Given: x = –2 is one zero of the polynomial `3x^2 + 4x + 2k`
Therefore, it will satisfy the above polynomial.
Now, we have 

`3(–2)^2 + 4(–2)1 + 2k = 0`
`⇒ 12 – 8 + 2k = 0`
`⇒ k = – 2`

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Polynomials - Exercises 3

APPEARS IN

R.S. Aggarwal Mathematics [English] Class 10
Chapter 2 Polynomials
Exercises 3 | Q 9

RELATED QUESTIONS

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).


The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).


Find the zeros of the polynomial `f(x) = x^2 + 7x + 12` and verify the relation between its zeroes and coefficients.


Find the zeroes of the quadratic polynomial `f(x) = 5x^2 ˗ 4 ˗ 8x` and verify the relationship between the zeroes and coefficients of the given polynomial.


Obtain all other zeroes of `(x^4 + 4x^3 – 2x^2 – 20x – 15)` if two of its zeroes are `sqrt5 and –sqrt5.` 


If -4 is a zero of the polynomial `x^2 – x – (2k + 2) is –4`, then find the value of k. 


Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.


If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then the product of the
other two zeroes is ______.


The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.


10. The zeroes of the quadratic polynomial x² + kx + k, k? 0.


If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then ______.


If x4 + 3x2 + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are ______.


If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as ______.


If one of the zeroes of the quadratic polynomial (k -1)x² + kx + 1 the value of k is ______.


Consider the following statements.

  1. x – 2 is a factor of x3 – 3x² + 4x – 4.
  2. x + 1 is a factor of 2x3 + 4x + 6.
  3. x – 1 is a factor of x5 + x4 – x3 + x² -x + 1.

In these statements


The number of polynomials having zeroes as -2 and 5 is ______.


The graph of y = f(x) is shown in the figure for some polynomial f(x).


The number of zeroes of f(x) is ______.


The zeroes of the quadratic polynomial 16x2 – 9 are ______.


If α and β are the zeroes of the polynomial x2 + x − 2, then find the value of `alpha/beta+beta/alpha`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×