Advertisements
Advertisements
Question
If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
If the graph of a polynomial intersects the x-axis at exactly two points.
Then it may or may not be a quadratic polynomial.
As, a polynomial of degree more than 2 is possible which intersects the x-axis at exactly two points when it has two real roots and other imaginary roots.
APPEARS IN
RELATED QUESTIONS
The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).
Find the zeroes of the polynomial `f(x) = x^2 ˗ 2x ˗ 8` and verify the relation between its zeroes and coefficients
One zero of the polynomial `3x^3+16x^2 +15x-18 is 2/3` . Find the other zeros of the polynomial.
Obtain all other zeroes of `(x^4 + 4x^3 – 2x^2 – 20x – 15)` if two of its zeroes are `sqrt5 and –sqrt5.`
If one zero of the polynomial `x^2-4x+1 is (2+sqrt3)` , write the other zero.
Find the zeroes of the polynomial `x^2 – 3x – m(m + 3)`
If 1is a zero of the quadratic polynomial `ax^2 – 3(a – 1)x – 1`is 1, then find the value of a.
If -2 is a zero of the polynomial `3x^2 + 4x + 2k` then find the value of k.
Find the sum of the zeros and the product of zeros of a quadratic polynomial, are `−1/2` and \ -3 respectively. Write the polynomial.
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
If one of the zeroes of the cubic polynomial x3 + px² + qx + r is -1, then the product of the other two zeroes is ______.
If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as ______.
Consider the following statements.
- x – 2 is a factor of x3 – 3x² + 4x – 4.
- x + 1 is a factor of 2x3 + 4x + 6.
- x – 1 is a factor of x5 + x4 – x3 + x² -x + 1.
In these statements
The number of polynomials having zeroes as -2 and 5 is ______.
If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.
The number of quadratic polynomials having zeroes –5 and –3 is ______.
The number of polynomials having zeroes – 3 and 4 is ______.
If α and β are the zeroes of the polynomial x2 + x − 2, then find the value of `alpha/beta+beta/alpha`
