Advertisements
Advertisements
प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
x2 – 2x – 8
Advertisements
उत्तर
By factorization method:
x2 - 2x - 8
⇒ x2 - 4x + 2x - 8 = 0
⇒ x(x - 4) + 2(x - 4) = 0
⇒ x(x - 4) + 2(x - 4) = 0
⇒ (x - 4) (x + 2) = 0
⇒ x - 4 = 0, x + 2 = 0
⇒ x = 4, x = -2
For p(x) = 0, we must have (x - 4) (x + 2) = 0 Either x - 4 = 0
x = 4
or x + 2 = 0
x = -2
∴ The zeroes of x2 - 2x - 8 are 4 and -2
Now,
= Sum of the zeroes `="-Coefficient of x"/"Coefficient of x"`
`-2+4=(-(-2))/1`
2 = 2 (L.H.S = R.H.S)
Product of the zeroes `="Constant term"/("Coefficient of "x^2)`
`-2xx4=(-8)/1`
`-8 = -8` (L.H.S = R.H.S)
Thus, the relationship between the zeroes and the coefficients in the polynomial x2 – 2x – 8 is verified.
APPEARS IN
संबंधित प्रश्न
Verify that the numbers given along side of the cubic polynomials are their zeroes. Also, verify the relationship between the zeros and the coefficients.
`f(x) = 2x^3 + x^2 - 5x + 2 ; 1/2, 1, - 2`
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
If α and β are the zeros of the quadratic polynomial f(x) = 6x2 + x – 2, find the value of `alpha/beta + beta/alpha`.
If a and 3 are the zeros of the quadratic polynomial f(x) = x2 + x − 2, find the value of `1/alpha-1/beta`.
Find the quotient and the remainder when f(x) = x4 – 3x2 + 4x + 5 is divided by g(x) = x2 – x + 1.
On dividing 3x3 + x2 + 2x + 5 is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
If α, β, γ are are the zeros of the polynomial f(x) = x3 − px2 + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]
If two zeros x3 + x2 − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
If the sum of the roots is –p and the product of the roots is `-1/"p"`, then the quadratic polynomial is:
An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.
The zeroes of the quadratic polynomial `4sqrt3"x"^2 + 5"x" - 2sqrt3` are:
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
`-2sqrt(3), -9`
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.
For the quadratic equation \[ ax^{2} + bx + c = 0 \] with roots \[ \alpha, \beta \], the sum of the roots \( \alpha + \beta \) equals:
A quadratic equation whose roots are \[ \alpha, \beta \] can be written as:
If a quadratic equation \[ ax^{2} + bx + c = 0 \] has roots \[ \alpha = 2 \] and \[ \beta = 3 \], which equation has exactly these roots?
