The zeros of the quadratic polynomial x2 + ax + h, a,b > 0 are
The correct answer is b
Given quadratic polynomial is,
p(x)=x2+ax+b
Let one of the zero of the polynomial is a then the other zero will be −a.
Sum of zeros=a+(−a)= −a / 1
=>0= −a/1
=>a=0
and product of the zeros =a(−a)=b/1
=>−a2=b
=>b=−a2
=>b has to be negative.
If p(x) = ax2 + bx + c and a + b + c = 0, then one zero is
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeros is
Let p(x) =ax3 + bx2 + cx + d
Given that, one of the zeroes of the cubic polynomial p(x) is zero.
Let α, β and γ are the zeroes of cubic polynomial p(x), where α = 0.
We know that,
Step-by-step explanation:
sum of two zeros at a time = c/a
∴αβ + βy + yα = c/a
∴0×β + βy + y×0 = c/a
βy = c/a
hence, product of 2 zeros = c/a
If p(x) = ax2 + bx + c and a + c = b, then one of the zeroes is
If one of the zeros of the quadratic polynomial (k - 1) x2 + k x + 1 is - 3, then the value of k is
The number of polynomials haying zeroes as -2 and 5 is
If one of the zeros of the cubic polynomial x3 + ax2 + bx + c is - 1, then the product of the other two zeroes 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
Let p(x) =ax3 + bx2 + cx + d
Given that, one of the zeroes of the cubic polynomial p(x) is zero.
Let α, β and γ are the zeroes of cubic polynomial p(x), where a = 0.
We know that,
Given that two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are 0, the value of c is
If 4x2 - 6x - m is divisible by x - 3, the value of m is exact divisor of
Here p(3) = 0
⇒ 4(3)2 - 6 x 3 - m = 0
⇒ 36 - 18 - m = 0 ⇒ m =18
∴ Value of m is exactly divisible by 9.
A quadratic polynomial, whose zeros are 5 and - 8 is
Which one of the following statements is correct
The zeros of the quadratic polynomial x2 + kx + k, k ≠ 0
Consider the following statements
(i) x - 2 is a factor of x3 - 3x2 + 4x - 4.
(ii) x + 1 is a factor of 2x3 + 4x + 6
(iii) x - 1 is a factor of x5 + x4 - x3 + x2 - x + 1
In these statements
x - 2 is a factor of x3 - 3x2 + 4x - 4
∵ remainder is zero
Similarly x + 1 is a factor of 2x3 + 4x + 6
but x - 1 is not a factor of x5 + x4 - x3 + x2 - x + 1
∵ remainder is not zero
∴ Statements 1 and 2 are correct.
The degree of the remainder r(x) when p (x) = bx3 + cx + d is divided by a polynomial of degree 4 is
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