The zeros of the quadratic polynomial x^{2} + 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) = ax^{2} + bx + c and a + b + c = 0, then one zero is
Given that one of the zeroes of the cubic polynomial ax^{3} + bx^{2} + 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,
Stepbystep 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) = ax^{2} + bx + c and a + c = b, then one of the zeroes is
If one of the zeros of the quadratic polynomial (k  1) x^{2} + 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 x^{3} + ax^{2} + bx + c is  1, then the product of the other two zeroes is
Given that one of the zeroes of the cubic polynomial ax^{3} + bx^{2} + cx + d is zero, the product of the other two zeroes is
Let p(x) =ax^{3} + bx^{2} + 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 ax^{3} + bx^{2} + cx + d are 0, the value of c is
If 4x^{2}  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 x^{2} + kx + k, k ≠ 0
Consider the following statements
(i) x  2 is a factor of x^{3}  3x^{2} + 4x  4.
(ii) x + 1 is a factor of 2x^{3} + 4x + 6
(iii) x  1 is a factor of x^{5} + x^{4}  x^{3} + x^{2}  x + 1
In these statements
x  2 is a factor of x^{3}  3x^{2} + 4x  4
∵ remainder is zero
Similarly x + 1 is a factor of 2x^{3} + 4x + 6
but x  1 is not a factor of x^{5} + x^{4}  x^{3} + x^{2}  x + 1
∵ remainder is not zero
∴ Statements 1 and 2 are correct.
The degree of the remainder r(x) when p (x) = bx^{3} + cx + d is divided by a polynomial of degree 4 is
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