Advertisements
Advertisements
Question
Find the zeroes of the polynomial `x^2 – 3x – m(m + 3)`
Advertisements
Solution
`f(x) = x^2 – 3x – m (m + 3)`
By adding and subtracting mx, we get
`f(x) = x^2 – mx – 3x + mx – m (m + 3)`
=` x[x – (m + 3)] + m[x – (m + 3)]`
= `[x – (m + 3)] (x + m)`
`f(x) = 0 ⇒ [x – (m + 3)] (x + m) = 0`
`⇒ [x – (m + 3)] = 0 or (x + m) = 0`
`⇒ x = m + 3 or x = –m`
So, the zeroes of f(x) are –m and +3.
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).
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) = x^2 + 3x ˗ 10` and verify the relation between its zeroes and coefficients.
Find all the zeroes of `(2x^4 – 3x^3 – 5x2 + 9x – 3)`, it is being given that two of its zeroes are `sqrt3 and –sqrt3`.
If one zero of the polynomial `x^2-4x+1 is (2+sqrt3)` , write the other zero.
If one zero of the quadratic polynomial `kx^2 + 3x + k is 2`, then find the value of k.
If -2 is a zero of the polynomial `3x^2 + 4x + 2k` then find the value of k.
If the sum of the zeros of the quadratic polynomial `kx^2-3x + 5` is 1 write the value of k..
Find the sum of the zeros and the product of zeros of a quadratic polynomial, are `−1/2` and \ -3 respectively. Write the polynomial.
If ∝ and β are the zeros of the polynomial f(x) = `6x^2 + x - 2 `find the value of `(∝/β+∝/β) `
If the zeroes of the polynomial `f(x) = x^3 – 3x^2 + x + 1` are (a – b), a and (a + b), find the values of a and b.
10. The zeroes of the quadratic polynomial x² + kx + k, k? 0.
A quadratic polynomial, whose zeores are -4 and -5, is ______.
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 the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.
The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0 ______.
The graph of y = f(x) is shown in the figure for some polynomial f(x).
The number of zeroes of f(x) is ______.
