Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If ЁЭЫ╝ and ЁЭЫ╜ are the zeros of the quadratic polynomial f(x) = x2 − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`
Advertisements
рдЙрддреНрддрд░
Since ЁЭЫ╝ ЁЭСОЁЭСЫЁЭСС ЁЭЫ╜ are the roots of the quadratic polynomial
f(x) = ЁЭСе2 − 5ЁЭСе + 4
Sum of roots = α + β = 5
Product of roots = αβ = 4
`1/alpha+1/beta-2alphabeta=(beta+alpha)/(alphabeta)-2alphabeta=5/4-2xx4=5/4-8=(-27)/4`
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
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
Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)` and `(2 - sqrt3)`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate :
`a(α^2/β+β^2/α)+b(α/β+β/α)`
If ЁЭЫ╝ and ЁЭЫ╜ are the zeros of the quadratic polynomial p(x) = 4x2 − 5x −1, find the value of α2β + αβ2.
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are α + 2, β + 2.
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
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:
If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is –3, then the value of k is ______.
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.
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`
Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`v^2 + 4sqrt(3)v - 15`
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
If α, β are zeroes of the quadratic polynomial x2 – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.
