(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 degree of the polynomial $p(x) = x^2 - x^3 + x + 1$ is $\ldots \ldots \ldots . .$

Easy

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If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} - 3x^{2} - 6x + 8$,then $\alpha \beta \gamma = \dots$

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

Medium

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The degree of $p(x) = \dots$ is $5$. Which of the following polynomials satisfies this condition?

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Obtain the cubic polynomial in the standard form with the following coefficients: $a=2, b=5, c=1, d=2$.

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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 degree of the polynomial $p(x) = x^2 - x^3 + x + 1$ is $\ldots \ldots \ldots . .$

If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} - 3x^{2} - 6x + 8$,then $\alpha \beta \gamma = \dots$

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

The degree of $p(x) = \dots$ is $5$. Which of the following polynomials satisfies this condition?

Obtain the cubic polynomial in the standard form with the following coefficients: $a=2, b=5, c=1, d=2$.

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