Advertisements
Advertisements
प्रश्न
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
उत्तर
`2sqrt3x^2-5x+sqrt3`
`2sqrt3x^2-2x-3x+sqrt3`
`2x(sqrt3x-1) or (2x-sqrt3=)=0`
`(sqrt3x-1)=0 or (2x-sqrt3)=0`
`x=1/sqrt3 or x=sqrt3/2`
`x=1/sqrt3xxsqrt3/sqrt3=sqrt3/3 or x=sqrt3/2`
Sum of zeroes= `sqrt3/3+sqrt2=(5sqrt3)/6 = -(("coefficient of" x))/(("coefficient of" x^2))`
Product of zeroes=`sqrt3/3xxsqrt3/2=sqrt3/6= ("constant term")/(("coefficient of "x^2))`
APPEARS IN
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
x2 – 2x – 8
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case
x3 – 4x2 + 5x – 2; 2, 1, 1
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`
If the zeros of the polynomial f(x) = x3 − 12x2 + 39x + k are in A.P., find the value of k.
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
If f(x) =` x^4 – 3x^2 + 4x + 5` is divided by g(x)= `x^2 – x + 1`
If 𝛼, 𝛽 are the zeroes of the polynomial `f(x) = 5x^2 -7x + 1` then `1/∝+1/β=?`
What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?
Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial ______.
If all three zeroes of a cubic polynomial x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative.
