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Q4. Find all zeroes of the polynomial 3x3 + 10x2 – 9x – 4, if one of its zeroes is 1. |
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Answer» All zeroes are 1 , -4 & -1/4 Step-by-step explanation:We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus,one factor of p(x) = ( x - 1 ) We get another factor of p(x) by dividing it with x - 1On division, quotient we get is 3x² + 13x + 4⇒p(x) = ( x - 1 ) ( 3x² + 13x + 4 )= ( x - 1 ) ( 3x² + 12x + x + 4 )= ( x - 1 ) [ 3x(x + 4) + (x + 4) ]= ( x - 1 ) ( x + 4 ) ( 3x + 1 )For zeroes put p(x) = 0⇒ ( x - 1 ) ( x + 4 ) ( 3x + 1 ) = 0x + 4 = 0& 3x + 1 = 0x = -4&x = -1/4Therefore,All zeroes are 1 , -4 & -1/4 |
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