Advertisements
Advertisements
प्रश्न
Find the sum of the zeros and the product of zeros of a quadratic polynomial, are `−1/2` and \ -3 respectively. Write the polynomial.
Advertisements
उत्तर
We can find the quadratic polynomial if we know the sum of the roots and product of the roots by using the formula
`x^2` – (sum of the zeroes)x + product of zeroes
We can find the quadratic polynomial if we know the sum of the roots and product of the roots by using the formula
`x^2 `– (sum of the zeroes)x + product of zeroes
`⇒ x^2-(-1/2)x+(-3)`
`⇒x^2+1/2x-3`
Hence, the required polynomial is `x^2+1/2x-3`
APPEARS IN
संबंधित प्रश्न
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) = 5x^2 ˗ 4 ˗ 8x` and verify the relationship between the zeroes and coefficients of the given polynomial.
Find the zeroes of the polynomial `x^2 – 3x – m(m + 3)`
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..
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.
Find the value of k such that the polynomial x2-(k +6)x+ 2(2k - 1) has some of its zeros equal to half of their product.
If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then ______.
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 ______.
A polynomial of degree n has ______.
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
If f(x) = 5x - 10 is divided by x – `sqrt2`, then the remainder will be ______.
If 4x² – 6x – m is divisible by x – 3, the value of m is exact divisor of ______.
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 zeroes of the polynomial 3x2 + 11x – 4 are ______.
The graph of y = f(x) is shown in the figure for some polynomial f(x).
The number of zeroes of f(x) is ______.
