Advertisements
Advertisements
Question
If 1 is a zero of the quadratic polynomial ax2 – 3(a – 1)x – 1 is 1, then find the value of a.
Advertisements
Solution
Given: x = 1 is one zero of the polynomial ax2 – 3(a – 1)x – 1
Therefore, it will satisfy the above polynomial.
Now, we have
a(1)2 – (a – 1)1 – 1 = 0
⇒ a – 3a + 3 – 1 = 0
⇒ –2a = –2
⇒ a = 1
APPEARS IN
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).
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 zeroes of the quadratic polynomial f(x) = x2 + 3x – 10 and verify the relation between its zeroes and coefficients.
If one zero of the polynomial x2 – 4x + 1 is `(2 + sqrt(3))`, write the other zero.
Find the zeros of the polynomial x2 + x – p(p + 1).
Write the zeros of the polynomial f(x) = x2 – x – 6.
If the sum of the zeros of the quadratic polynomial kx2 – 3x + 5 is 1, write the value of k.
Find the value of k such that the polynomial x2 − (k + 6)x + 2(2k −1) has sum of its zeros equal to half of their product.
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, 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 one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it ______.
A quadratic polynomial, whose zeores are -4 and -5, is ______.
Consider the following statements.
- x – 2 is a factor of x3 – 3x² + 4x – 4.
- x + 1 is a factor of 2x3 + 4x + 6.
- 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 ______.
Which of the following is not the graph of a quadratic polynomial?
If α and β are the zeroes of the polynomial x2 – 1, then the value of (α + β) is ______.
The graph of y = f(x) is shown in the figure for some polynomial f(x). The number of zeroes of f(x) are ______.
