## Find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively

[question] Question. Find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively (i) $\frac{1}{4},-1$ (ii) $\sqrt{2}, \frac{1}{3}$ (iii) $\mathbf{0}, \sqrt{\mathbf{5}}$ (iv) 1,1 $(V)-\frac{1}{4}, \frac{1}{4}$ (vi) 4,1 [/question] [solution] Solution: (i) Required polynomial = $x^{2}-($ sum of zeros $) x+$ product of zeros $=x^{2}-\frac{1}{4} x-1$ $=\frac{1}{4}\left(4 x^{2}-x-1\right)$ (ii) Required polynomial = $x^{2}-($ sum of zeros $) x+$ product of...

## Find the zeros of the following quadratic polynomials and verify

[question] Question. Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients. (i) $x^{2}-2 x-8$ (ii) $4 \mathrm{~s}^{2}-4 \mathrm{~s}+1$ (iii) $6 x^{2}-3-7 x$ (iv) $4 u^{2}+8 u$ (v) $t^{2}-15$ (vi) $3 x^{2}-x-4$ [/question] [solution] Solution: (i) $x^{2}-2 x-8=x^{2}-4 x+2 x-8$ $=x(x-4)+2(x-4)=(x+2)(x-4)$ Zeroes are – 2 and 4. Sum of the zeros \$=(-2)+(4)=2=\frac{-(-2)}{1}=\frac{-(\text { Coefficient of } \mathbf{x})}{\left(\text { ...