Find the zeroes of the polynomial p(x)=2x²+7x+3
Answers
3 and 1/2( answer )
Step-by-step explanation:
finding a zero of a polynomial means that the value of the variable/X should be something which when put into the polynomial makes the polynomial 0...
so we will take
p(X) = 2x^2+7x+3 = 0
we will have to use completing square method (you will understand it better by searching online or watching a YouTube video)
p(X) = 2x^2+7x = -3
p(X) = (2x^2+7x)/2 = -3/2(divide both sides by 2 according to the method)
p(X) = x^2+7/2x = -3/2
then we have to add (1/2 × coefficient of X)^2 on both sides
(1/2×7/2)^2 = (7/4)^2 = 49/16
p(X) = x^2+7/2x+49/16 = -3/2+49/16
p(X) = (X+7/4)(X+7/4) = (49-24)/16(identity:- (a+b)^2 = a^2+2ab+b^2)
p(X) = (X+7/4)^2 = 25/16
p(X) = (X+7/4) = +/-√(25/16)
p(X) = X+7/4 = +/- 5/4
p(X) = X = 7/4+/- 5/4
therfore the zeroes are
1) 7/4+5/4=12/4=3
2) 7/4-5/4=2/4=1/2
I hope you understood the explanation and we divided both sides by two and added both side with (1/2×coefficient of X)^2 to make it an identity and make it easier for us to solve and this method is called completing square method.
Answer:
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