Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
Advertisements
उत्तर
6x2 – 7x – 3 = 0
⇒ 6x2 – 9x + 2x – 3 = 0
⇒ 3x(2x – 3) + 1(2x – 3) = 0
⇒ (2x – 3)(3x + 1) = 0
⇒ 2x – 3 = 0 and 3x + 1 = 0
⇒ 2x = 3 and 3x = −1
⇒ x = `3/2` and x = `(-1)/3`
Let considered x = `3/2` be α and x = `(-1)/3` be β.
α + β = `3/2 + ((-1)/3) = (9 - 2)/6 = 7/6`
`(-"b")/"a" = (-(-7))/6 = 7/6`
⇒ α + β = `(-"b")/"a"`
αβ = `3/2 xx (-1)/3 = (-1)/2`
`"c"/"a" = (-3)/6 = (-1)/2`
αβ = `"c"/"a"`
APPEARS IN
संबंधित प्रश्न
if α and β are the zeros of ax2 + bx + c, a ≠ 0 then verify the relation between zeros and its cofficients
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
3x2 – x – 4
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`0, sqrt5`
If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± `sqrt3` , find other zeroes
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 α and β are the zeros of the quadratic polynomial f(x) = 6x2 + x – 2, find the value of `alpha/beta + beta/alpha`.
Find the zeroes of the quadratic polynomial 4x2 – 4x + 1 and verify the relation between the zeroes and the coefficients.
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
What should be added to the polynomial x2 − 5x + 4, so that 3 is the zero of the resulting polynomial?
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
