(D) Given the polynomial $p(x) = x^{2} + x + k$.According to the Factor Theorem,if $(x - 1)$ is a factor of $p(x)$,then $p(1)$ must be equal to $0$.Su

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(D) Given the polynomial $p(x) = x^{2} + x + k$.According to the Factor Theorem,if $(x - 1)$ is a factor of $p(x)$,then $p(1)$ must be equal to $0$.Substituting $x = 1$ into the polynomial:$p(1) = (1)^{2} + 1 + k$$p(1) = 1 + 1 + k$$p(1) = 2 + k$Since $p(1) = 0$,we have:$2 + k = 0$$k = -2$

Class 9 Mathematics Polynomials Textbook - Polynomials

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Find the value of $k$,if $x - 1$ is a factor of $p(x)$ in this case: $p(x) = x^{2} + x + k$.

A
$0$
B
$3$
C
$2$
D
$-2$

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Polynomials

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Textbook - Polynomials

Write the coefficients of $x^2$ in each of the following:
$(i)$ $\frac{\pi}{2} x^2 + x$
$(ii)$ $\sqrt{2} x - 1$

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Use suitable identities to find the product: $\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)$

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Check whether $-2$ and $2$ are zeroes of the polynomial $x + 2$.

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Use suitable identities to find the products: $(x+8)(x-10)$

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Factorise: $x^{3}+13x^{2}+32x+20$

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Find the value of $k$,if $x - 1$ is a factor of $p(x)$ in this case: $p(x) = x^{2} + x + k$.

Similar Questions

Write the coefficients of $x^2$ in each of the following:$(i)$ $\frac{\pi}{2} x^2 + x$$(ii)$ $\sqrt{2} x - 1$

Use suitable identities to find the product: $\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)$

Check whether $-2$ and $2$ are zeroes of the polynomial $x + 2$.

Use suitable identities to find the products: $(x+8)(x-10)$

Factorise: $x^{3}+13x^{2}+32x+20$

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Write the coefficients of $x^2$ in each of the following:
$(i)$ $\frac{\pi}{2} x^2 + x$
$(ii)$ $\sqrt{2} x - 1$