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Write sum and product of zero of polynomial 12x^3-4x²-3x+ |
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Answer» Step-by-step explanation: In the given polynomial 4X2+12x+5, The first TERM is 4x2 and its coefficient is 4. The middle term is 12x and its coefficient is 12. The last term is a constant term 5. Multiply the coefficient of the first term by the constant 4×5=20. We now find the factor of 20 whose SUM equals the coefficient of the middle term, which is 12 and then factorize the polynomial 4x2+12x+5 and equate it to 0 as shown below:
4x2+12x+5=0⇒4x2+2x+10x+5=0⇒2x(2x+1)+5(2x+1)=0⇒(2x+1)(2x+5)=0⇒2x=−1,2x=−5⇒x=−21,x=−25 Therefore, the zeroes of the polynomial 4x2+12x+5 are −1,34. Now, the sum and the product of the zeroes of the given quadratic polynomial is as follows: =》 -1/2+(-5/2)= -1/2 -5/2= -6/2= -3 =》(-1/2)×(-5/2)=1/2×5/2= 5/4 =》Hence, the sum of the ZEROS is -3 and the product of zeros is 5/4. |
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