Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial `f(x) = x^2 + 3x ˗ 10` and verify the relation between its zeroes and coefficients.
उत्तर
We have:
`f(x) = x^2 + 3x ˗ 10`
=` x^2 + 5x ˗ 2x ˗ 10`
= x(x + 5) ˗ 2(x + 5)
= (x ˗ 2) (x + 5)
∴ f(x) = 0 ⇒ (x ˗ 2) (x + 5) = 0
⇒ x ˗ 2 = 0 or x + 5 = 0
⇒ x = 2 or x = −5.
So, the zeroes of f(x) are 2 and −5.
Sum of zeroes= `2+(-5)=-3=(-3)/1="(-coefficient of x)" /(("Coefficent of "x^2))`
Product of zeroes =`2xx(-5)=-10=(-10)/1= "Constant term"/(("Coefficcient of "x^2 ))`
APPEARS IN
संबंधित प्रश्न
Obtain all other zeroes of `(x^4 + 4x^3 – 2x^2 – 20x – 15)` if two of its zeroes are `sqrt5 and –sqrt5.`
If -4 is a zero of the polynomial `x^2 – x – (2k + 2) is –4`, then find the value of k.
If 1is a zero of the quadratic polynomial `ax^2 – 3(a – 1)x – 1`is 1, then find the value of a.
Find the zeroes of the quadratic polynomial `f(x) = 6x^2 – 3.`
If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is ______.
If x4 + 3x2 + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are ______.
If f(x) = 5x - 10 is divided by x – `sqrt2`, then the remainder will be ______.
If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.
If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then ______.
The zeroes of the quadratic polynomial 16x2 – 9 are ______.
