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If x + 2 is a factor of x^{3} – 2ax^{2} + 16, then value of a is
x²+ 5x  6 = 0
x²  x + 6x  6
x (x1) + 6 (x1)
(x1) (x+6)
x = 1; x = 6
If 3 + 5 – 8 = 0, then the value of (3)^{3} + (5)^{3} – (8)^{3} is
3^3+5^38^3=27+125512
=152512
=360
⇒ x²+ 5x  6 = 0
⇒ x²+ 6x x  6 = 0
⇒ x(x+6) 1(x+6) = 0
⇒ (x1) (x+6) = 0
⇒ x = 1, 6
If x + 2 is a factor of x^{3} – 2ax^{2} + 16, then value of a is
use factor theorem as x+2 is factor of
x³2ax²+16 so put x = 2 and equate the equation to 0
so putting x = 2
(2)³2a(2)²+16 =0
88a+16=0
8a = 8
a = 8/8= 1
So,
a = 1
Which of the following is not a quadratic polynomial?
P of x = ax, a is not equal to 0. find zeros of polynmial
p(x) = ax
p(x) = 0
ax = 0
x = 0/a
x = 0
{0 by something is equals to 0}
Therefore,0 is the zero of the polynomial.
Checking:
p(0) = a(0)
= 0
Zero of the polynomial p(x) where p (x) = ax, a ≠ 0 is:
If x + 2 is a factor of x^{3} – 2ax^{2} + 16, then value of a is
If p(x) = 7 – 3x + 2x^{2} then value of p(2) is:
p(2) = 7  3(2) + 2(2)^{2}
= 7+6+8 = 21
A linear polynomial has 1 zero.
A quadratic polynomial has 2 zeroes.
A cubic polynomial has 3 zeroes.
In general, any polynomial has as many zeroes as its degree.
If one of the factor of x^{2} + x – 20 is (x + 5). Find the other
Which of the following is a quadratic polynomial in one variable?
A cubic polynomial is a polynomial of degree …………
A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form An equation involving a cubic polynomial is called a cubic equation. A closedform solution known as the cubic formula exists for the solutions of an arbitrary cubic equation.
Find the value of the polynomial 6 – 4x + 3x^{2} at x = 3
A zero polynomial is a polynomial in which all the coefficients are 0.
Let the polynomials highest power variable be x^n as per the above statement x^n = 0
Now, The degree of the zero polynomial is log0 which is undefined.
Hence. The degree of zero polynomial is undefined.
Zero of the zero polynomial is any real number.
e.g., Let us consider zero polynomial be 0(xk), where k is a real number For determining the zero, put xk = 0 ⇒ x = k Hence, zero of the zero polynomial be any real number.
What is the coefficient of x in x^{3} + 3x^{2}  2x  1
The degree of the polynomial x^{4} – 3x^{3} + 2x^{2} – 5x + 3 is:
The degree refers to the highest power of the polynomial. In this polynomial X has highest power 4.So the degree of polynomial is 4.
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