58786.If the zeroes of the quadratic polynomial $ax^2+bx+c$, c≠0 are equal, then
c and b have opposite signs
c and a have opposite signs
c and b have same signs
c and a have same signs
Explanation:
For equal roots, discriminant will be equal to zero.
$b^2$ -4ac = 0
$b^2$ = 4ac
ac = $\dfrac{b^2}{4}$
ac>0 (as square of any number cannot be negative)
58787.The degree of the polynomial, $x^4 – x^2 +2$ is
2
4
1
0
Explanation:
Degree is the highest power of the variable in any polynomial.
58788.If p(x) is a polynomial of degree one and p(a) = 0, then a is said to be:
Zero of p(x)
Value of p(x)
Constant of p(x)
None of the above
Explanation:
Let p(x) = mx+n
Put x = a
p(a)=ma+n=0
So, a is zero of p(x).
58789.Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of
polynomial is:
Intersects x-axis
Intersects y-axis
Intersects y-axis or x-axis
None of the above
58790.Given that two of the zeroes of the cubic polynomial $ax^3 + bx^2 + cx + d$ are 0, the third zero is
$\dfrac{-b}{a}$
$\dfrac{b}{a}$
$\dfrac{c}{a}$
$\dfrac{-d}{a}$
Explanation:
Let α be the third zero.
Given that two zeroes of the cubic polynomial are 0.
Sum of the zeroes = α + 0 + 0 = $\dfrac{-b}{a}$
α = $\dfrac{-b}{a}$
58791.If one zero of the quadratic polynomial $x^2 + 3x + k$ is 2, then the value of k is
10
–10
5
–5
Explanation:
Given that 2 is the zero of the quadratic polynomial $x^2 + 3x + k.$
$(2)^2$ + 3(2) + k = 0
4 + 6 + k = 0
k = -10
58792.The zeroes of the quadratic polynomial $x^2 + 7x + 10$ are
-4, -3
2, 5
-2, -5
-2, 5
Explanation:
$x^2$ + 7x + 10 = $x^2$ + 2x + 5x + 10
= x(x + 2) + 5(x + 2)
= (x + 2)(x + 5)
Therefore, -2 and -5 are the zeroes of the given polynomial.
58793.By division algorithm of polynomials, p(x) =
g(x) × q(x) + r(x)
g(x) × q(x) – r(x)
g(x) × q(x) × r(x)
g(x) + q(x) + r(x)
Explanation:
By division algorithm of polynomials, p(x) = g(x) × q(x) + r(x).
58794.The product of the zeroes of the cubic polynomial $ax^3 + bx^2 + cx + d$ is
$\dfrac{-b}{a}$
$\dfrac{c}{a}$
$\dfrac{-d}{a}$
$\dfrac{-c}{a}$
Explanation:
The product of the zeroes of the cubic polynomial $ax^3 + bx^2 + cx + d$ is $\dfrac{-d}{a}$
