Find the zeros of a quadratic polynomial √3x2 - 8x + 4√3.
We should factorize the equation first. =√3x² - 6x - 2x + 4√3 = 0
= √3x(x - 2√3) - 2(x - 2√3) = 0
= (√3x - 2) (x - 2√3) = 0
= (√3x - 2) = 0, (x - 2√3) = 0
= x = 2 / √3 , x = 2√3.
Write the degree of the given polynomial: 2p - √7.
Find the degree of the polynomial 5t + √7.
Find the smallest solution in positive integers of x2 - 14y2 = 1.
Now checking by putting y = 1, 2, 3... until we get solution
y = 1; => x2 =15 not possible
y = 2; => x2 = 57 not possible
y = 3; => x2 = 127 not possible
y = 4; => x2 = 225 => x = 15
Hence, the smallest solution is (x, y) = (15, 4).
Find the zeroes of the quadratic polynomial from the graph.
If one zero of polynomial (k2 + 16) x2 + 16x + 8k is reciprocal of the other, them k is equal to
The graph of f(x) is shown below. The number of zeroes of f(x) are:
The graph of a quadratic polynomial p(x) = ax2 + bx + c is a parabola, opening downwards if
Sum of the zeroes of the polynomial p(x) = - 3x2 + a is
The sum and product of zeroes of a quadratic polynomial are - 1 and - 6 respectively. The quadratic polynomial is given by
p(x) = x² - x (sum of zeros) + product of zeros
p(x) = x² - x (-1) + (-6)
p(x) = x² + x - 6
Number of zeroes of a polynomial of degree n is
Number of quadratic polynomials having - 2 and - 5 as their two zeroes is
Hence, the required number of polynomials are infinite i.e., more than 3.
Which of the following is not a graph of a quadratic polynomial?
If one zero of the quadratic polynomial 39 y2 - (2k + 1)y - 22 is negative of the other, then the value of k is
If α and β are zeros of a quadratic polynomial such that α + β = 12 and α - β = 6. Them, the family of quadratic polynomials having α, β as its zeroes is given by
If α, β, γ are the zeroes of the polynomial p(x) = x3 + 6x2 + cx + d, such that α + β = 2, then the value of γ is
⇒ α + β + γ = −6
⇒ 2 + γ = −6
⇒ γ = −8
If the zeroes of the quadratic polynomial x2 + (a +1) x + b are 2 and - 3, then
=> 1 (a + 1) = 1
=> a + 1 = 1
=> a = 0
Also, 2 × (−3) = b = -6
When x4 + x3 - 2x2 + x + 1 is divided by x - 1, them the remainder is
If α and β are the zeroes of the quadratic polynomial p(x) = x2 + 2x - k such that α2 + β2 = 34, then the value of k is
α + β = -2
α x β = c / a
α x β = -k
Now, α2 + β2 = 34
using identity we get
(α + β)2 - 2α x β
Now putting up the values
(-2)2 - 2 x -k = 34
4 + 2k = 34
2k = 30
k = 15.
Product of the zeros of the cubic polynomial P(x) = kx3 − 5x2 − 12x + k
product of roots ax3 + bx2 + cx + d = 0
is -d / a
product of polynomials = -k / k = -1