Practice the questions given in the worksheet on application of Factor Theorem.
1. Find the roots of the equation 6z\(^{2}\) + 11z 10 = 0. Hence, factorize 6z\(^{2}\) + 11z 10.
2. Find the roots of the equation 2m\(^{2}\)  3m  6 = 0. Hence, factorize 2m\(^{2}\)  3m  6 = 0
3. Find the roots of the equation p(p + 1)  4 = 0. Hence, factorize 4  p  p\(^{2}\).
4. Find the quadratic equation whose roots are
(i) 3, 7
(ii) 2 + √3, 2  √3
(iii) \(\frac{1}{√3}\),  \(\frac{1}{√3}\)
5. Find the cubic equation whose roots are
(i) 1, 2, 3
(ii) 4, √3, √3
(iii) \(\frac{1}{2}\), \(\frac{√5}{2}\), \(\frac{√5}{2}\)
Answers for the worksheet on application of Factor Theorem are given below:
Answers:
1. \(\frac{2}{3}\) , \(\frac{5}{2}\); (3z  2)(2z + 5)
2. \(\frac{3 + √57}{4}\), \(\frac{3  √57}{4}\); (2m  \(\frac{3 + √57}{2}\))(m  \(\frac{3  √57}{4}\))
3. \(\frac{1 + √17}{2}\), \(\frac{1  √17}{2}\); (\(\frac{1 + √17}{2}\)  p)( \(\frac{1 + √17}{2}\) + p)
4. (i) y\(^{2}\)  4y 21 = 0
(ii) z\(^{2}\)  4z + 1 = 0
(iii) 3p\(^{2}\)  1 = 0
5. (i) z\(^{3}\)  6z\(^{2}\) + 11z  6
(ii) m\(^{3}\) + 4m\(^{2}\)  3m  12
(iii) 8k\(^{3}\)  4k\(^{2}\)  10k + 5 = 0
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