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).
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
Find the zeroes of the quadratic polynomial `f(x) = x^2 + 3x ˗ 10` and verify the relation between its zeroes and coefficients.
One zero of the polynomial `3x^3+16x^2 +15x-18 is 2/3` . Find the other zeros of the polynomial.
Find ∝ , β are the zeros of polynomial ∝ +β= 6 and ∝β 4 then write the polynomial.
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`.
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 one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then the product of the
other two zeroes is ______.
10. The zeroes of the quadratic polynomial x² + kx + k, k? 0.
If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then ______.
If x4 + 3x2 + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are ______.
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
The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0 ______.
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
If α and β are the zeroes of the polynomial x2 + x − 2, then find the value of `alpha/beta+beta/alpha`
