(A) linear polynomial is defined as $p(x) = ax + b$,where $a \neq 0$.To find the intersection with the $X$-axis,we set $p(x) = 0$.$ax + b = 0$$ax = -b

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(A) linear polynomial is defined as $p(x) = ax + b$,where $a \neq 0$.To find the intersection with the $X$-axis,we set $p(x) = 0$.$ax + b = 0$$ax = -b$$x = -b/a$Since $a \neq 0$,there is exactly one unique value of $x$ for which $p(x) = 0$.Therefore,the graph of a linear polynomial intersects the $X$-axis at exactly one point,which is $(-b/a, 0)$.

Class 10 Mathematics Polynomials Mix Examples - Polynomials

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The graph of a linear polynomial $p(x) = ax + b$ intersects the $X$-axis at $\ldots \ldots \ldots \ldots$ (where $a \neq 0$).

A
one point
B
two distinct points
C
does not intersect
D
three distinct points

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Mix Examples - Polynomials

The value of $p(x) = 2x^{4} - 3x^{3} + 7x + 5$ at $x = -2$ is $\ldots \ldots \ldots \ldots$

Easy

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Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$y^{2}+\frac{3}{2} \sqrt{5} y-5$

Medium

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The graph of $\ldots \ldots \ldots \ldots$ is a curve open downwards.

Easy

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Answer the following and justify:
Can the quadratic polynomial $x^{2}+kx+k$ have equal zeroes for some odd integer $k > 1$?

Medium

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The product of two polynomials is $x^{3}-3x^{2}-x+3$ and one of the polynomials is $x+1$. Find the other polynomial.

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The graph of a linear polynomial $p(x) = ax + b$ intersects the $X$-axis at $\ldots \ldots \ldots \ldots$ (where $a \neq 0$).

Similar Questions

The value of $p(x) = 2x^{4} - 3x^{3} + 7x + 5$ at $x = -2$ is $\ldots \ldots \ldots \ldots$

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:$y^{2}+\frac{3}{2} \sqrt{5} y-5$

The graph of $\ldots \ldots \ldots \ldots$ is a curve open downwards.

Answer the following and justify:Can the quadratic polynomial $x^{2}+kx+k$ have equal zeroes for some odd integer $k > 1$?

The product of two polynomials is $x^{3}-3x^{2}-x+3$ and one of the polynomials is $x+1$. Find the other polynomial.

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Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$y^{2}+\frac{3}{2} \sqrt{5} y-5$

Answer the following and justify:
Can the quadratic polynomial $x^{2}+kx+k$ have equal zeroes for some odd integer $k > 1$?