Advertisements
Advertisements
प्रश्न
Define a polynomial with real coefficients.
उत्तर
In the polynomial `f(x)=a_nx^n+a_(n-1)+......+a_1x+a_o`,
`a_nx^n,a_(n-1x^(n-1)...,a_1x`, and `a_0`are known as the terms of the polynomial and `a_n,a_(n-1),...,a_1`and `a_0` are their real coefficients.
For example, `p(x)=3x-2` is a polynomial and 3 is a real coefficient
APPEARS IN
संबंधित प्रश्न
Prove relation between the zeros and the coefficient of the quadratic polynomial ax2 + bx + c
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) = ax3 + 3bx2 + 3cx + d are in A.P., prove that 2b3 − 3abc + a2d = 0.
Find the quadratic polynomial whose zeroes are `2/3` and `-1/4` Verify the relation between the coefficients and the zeroes of the polynomial.
If f(x) =` x^4 – 3x^2 + 4x + 5` is divided by g(x)= `x^2 – x + 1`
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
If two zeros x3 + x2 − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is
Case Study -1
The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.
Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time ‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t2 + 8t + k.
The zeroes of the polynomial r(t) = -12t2 + (k - 3)t + 48 are negative of each other. Then k is ______.
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
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`
