Advertisements
Advertisements
प्रश्न
If ∝ and β are the zeros of the polynomial f(x) = `6x^2 + x - 2 `find the value of `(∝/β+∝/β) `
Advertisements
उत्तर
By using the relationship between the zeroes of the quadratic polynomial.
We have
Sum of zeroes=`(-("Coefficent of x"))/("Coefficient of" x^2)` and Product of zeroes = `"Constant term"/("Coefficient of" x^2)`
∴ 𝛼 + 𝛽=`-1/6` and 𝛼𝛽 =`-1/3`
Now, `∝/β+β/∝=(∝^2+β^2)/(∝β)`
`= (∝^2+β^2+2∝β-2∝β)/(∝β)`
`=((∝+β)^2-2∝β)/(∝β)`
`=((-1/6)^2-2(1/3))/(1/3)`
`=(1/36+2/3)/ (1/3)`
`=-25/12`
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), in the following.
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.
Find the zeroes of the polynomial `x^2 + x – p(p + 1) `
If 3 is a zero of the polynomial `2x^2 + x + k`, find the value of k.
Write the zeros of the polynomial `f(x) = x^2 – x – 6`.
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 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.
If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and –3, then ______.
The number of polynomials having zeroes as -2 and 5 is ______.
If x3 + 11 is divided by x2 – 3, then the possible degree of remainder is ______.
If x4 + 3x2 + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are ______.
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 ______.
The number of polynomials having zeroes as -2 and 5 is ______.
If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.
If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.
