Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
We have:
`f(x) = 5x^2 ˗ 4 ˗ 8x`
`= 5x^2 ˗ 8x ˗ 4`
`= 5x^2 ˗ (10x ˗ 2x) ˗ 4`
`= 5x^2 ˗ 10x + 2x ˗ 4`
`= 5x (x ˗ 2) + 2(x ˗ 2)`
`= (5x + 2) (x ˗ 2)`
∴ f(x) = 0 ⇒ (5x + 2) (x ˗ 2) = 0
⇒ 5x + 2= 0 or x ˗ 2 = 0
`⇒ x = (−2)/5 or x = 2 `
So, the zeroes of f(x) are `((−2)/5)` and 2
Sum of zeroes =`((-2)/5)+2=(-2+10)/5=8/5="(-Coefficient of x)"/(("Coefficient of" x^2))`
Product of zeroes=`((-2)/5)xx2=(-4)/5= "Constant term"/(("Coefficient of" x^2))`
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 polynomial `f(x) = x^2 ˗ 2x ˗ 8` and verify the relation between its zeroes and coefficients
If f(x) =`x^3-3x+5x-3` is divided by g(x)=`x^2-2`
Find the zeroes of the polynomial `x^2 + x – p(p + 1) `
If 𝛼 and 𝛽 be the zeroes of the polynomial `2x^2 - 7x + k` write the value of (𝛼 + 𝛽 + 𝛼𝛽).
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 one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k 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 ______.
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
10. The zeroes of the quadratic polynomial x² + kx + k, k? 0.
A quadratic polynomial, whose zeores are -4 and -5, is ______.
The zeroes of the quadratic polynomial x² + 1750x + 175000 are ______.
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
The number of polynomials having zeroes as -2 and 5 is ______.
If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.
If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then ______.
The number of polynomials having zeroes – 3 and 4 is ______.
The zeroes of the quadratic polynomial 16x2 – 9 are ______.
The graph of y = f(x) is shown in the figure for some polynomial f(x). The number of zeroes of f(x) are ______.
The given linear polynomial y = f(x) has
