If 𝛼, 𝛽 Are the Zeroes of the Polynomial `F(X) = X^2 – 5x + K` Such that 𝛼 - 𝛽 = 1, Find the Value of K = ? - Mathematics

If 𝛼, 𝛽 are the zeroes of the polynomial `f(x) = x^2 – 5x + k` such that 𝛼 - 𝛽 = 1, find the value of k = ?

By using the relationship between the zeroes of the quadratic polynomial.
We have

Sum of zeroes=`(-("Coefficent of x"))/("Cofficient of x"^2)` and Product of zeroes =`("Constant term")/("Coefficent of "x^2)`

`∴ ∝+β=-(-5)/1` and ∝β=k/1`

Solving 𝛼 - 𝛽 = 1 and 𝛼 + 𝛽 = 5, we will get

∝=3 and 𝛽=2

Substituting these values in 𝛼𝛽 =`k/1` we will get

`k = 6`

shaalaa.com

Is there an error in this question or solution?

Chapter 2 Polynomials
Exercises 3 | Q 21

Find the zeroes of the polynomial `f(x) = x^2 ˗ 2x ˗ 8` 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`.

Find the zeroes of the polynomial `x^2 – 3x – m(m + 3)`

If one zero of the quadratic polynomial `kx^2 + 3x + k is 2`, then find 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.

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

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

The zeroes of the quadratic polynomial x² + 1750x + 175000 are ______.

If x³ + 11 is divided by x² – 3, then the possible degree of remainder is ______.

If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.