Advertisements
Advertisements
प्रश्न
If one zero of the polynomial `x^2-4x+1 is (2+sqrt3)` , write the other zero.
Advertisements
उत्तर
Let the other zeroes of `x^2 – 4x + 1` be a.
By using the relationship between the zeroes of the quadratic polynomial.
We have, sum of zeroes =`(-("Coefficient of x"))/(("Coefficient of" x^2))`
∴` 2+sqrt3+a=-((-4))/1`
⇒` a = 2 – sqrt3`
Hence, the other zeroes of` x^2 – 4x + 1 is 2 – sqrt3`
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.
If one zero of the quadratic polynomial `kx^2 + 3x + k is 2`, then find the value of k.
If -4 is a zero of the polynomial `x^2 – x – (2k + 2) is –4`, then find the value of k.
Write the zeros of the polynomial `f(x) = x^2 – x – 6`.
Find the zeroes of the quadratic polynomial `f(x) = 6x^2 – 3.`
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 = ?
If ∝ and β are the zeros of the polynomial f(x) = `6x^2 + x - 2 `find the value of `(∝/β+∝/β) `
The number of polynomials having zeroes as -2 and 5 is ______.
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then the product of the
other two zeroes is ______.
If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then ______.
If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it ______.
If x3 + 1 is divided by x2 + 5, then the possible degree of quotient is ______.
If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as ______.
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 4x² – 6x – m is divisible by x – 3, the value of m is exact divisor of ______.
If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.
The given linear polynomial y = f(x) has
