Question

If 2 is a zero of the polynomial $$p\left( x\right) =2x^{2}-3x+7a$$, find the value of a.

Answer 1

Hint: In this question it is given that we have to find the value of a, where 2 is the zero of the polynomial $$p\left( x\right) =2x^{2}-3x+7a$$. Since 2 is the zero of the polynomial so we have to put x=2 in the given polynomial which gives zero, from where we are able to get the value of a.

Complete step-by-step answer:
Here it is given that 2 is the zero of the given polynomial.
Therefore, if we put x=2 then the polynomial becomes zero.
i,e, for x=2, p(2)=0,
$$\therefore p\left( 2\right) =0$$
$$\Rightarrow 2\times 2^{2}-3\times 2+7a=0$$
On simplifying this, we get
$$\Rightarrow 2\times 4-6+7a=0$$
$$\Rightarrow 8-6+7a=0$$
$$\Rightarrow 2+7a=0$$
$$\Rightarrow 7a=-2$$
Dividing 7 on both the sides,
$$\Rightarrow a=\dfrac{-2}{7}$$
Therefore the value of a is $$\dfrac{-2}{7}$$.

Note: While solving this type of question you need to know that for a polynomial, there could be some values of the variable for which the polynomial will be zero. These values are called zeros of a polynomial. Sometimes, they are also referred to as roots of the polynomials. In general, we used to find the zeros of quadratic equations, also the given polynomial is also a quadratic polynomial because in the algebraic expression the highest power of x is 2 and every quadratic polynomial has at most two zeros.