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##### 4. Solve by using synthetic division if(ii) 3 is the root of the equation 2 x^{3}-3 x^{2}-11 x+6=0

(x) \alpha^{2}+\beta^{2} is equal to(a) \alpha^{2}-\beta^{2} (b) \frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}} (c) (\alpha+\beta)^{2}-2 \alpha \beta (d) \alpha+\beta

(ix) \frac{1}{\alpha}+\frac{1}{\beta} is equal to(a) \frac{1}{\alpha} (b) \frac{1}{\alpha}-\frac{1}{\beta} (c) \frac{\alpha-\beta}{\alpha \beta} (d). \frac{\alpha+\beta}{\alpha \beta}

4. Find p if(ii) the roots of the equation x^{2}+3 x+p-2=0 differ by 2 .

2 . Evaluate(i) \left(1-\omega-\omega^{2}\right)^{7}

1. Without solving find the sum and the product of the roots of the following ratic equations.(ii) 3 x^{2}+7 x-11=0

6. Find m if sum and product of the roots of the following equations is equal to a given number \lambda .(ii) 4 x^{2}-(3+5 m) x-(9 m-17)=0