d)f(x) = 6x^2 − 3 − 7x
e) p(x) = x^2 + 2√2x − 6
f) q(x) = √3x^2 + 10x + 7√3
g) f(x) = x^2 − (√3 + 1)x + √3
h) g(x) = a(x^2 + 1) − x(a^2 + 1)
help . Give correct answers
Answers
Answer:
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Step-by-step explanation:
Solutions :-
d)
Given expresion is f(x) = 6x^2 − 3 − 7x
=> f(x) = 6x²-7x-3
=> f(x) = 6x²+2x-9x-3
=> f(x) = 2x(3x+1)-3(3x+1)
=> f(x) = (3x+1)(2x-3)
Factorization of f(x) = (3x+1)(2x-3)
To get zeroes we write f(x) = 0
=> (3x+1)(2x-3)=0
=> 3x+1 = 0 or 2x-3 = 0
=> 3x = -1 or 2x = 3
=> x = -1/3 or x = 3/2
Zeroes are -1/3 and 3/2
e)
Given expresion is p(x) = x^2 + 2√2x − 6
=> p(x) = x² + 2√2x − 6
=> p(x) = x²+3√2x-√2x - 6
=> p(x) = x(x+3√2)-√2(x+3√2)
=> p(x) = (x+3√2)(x-√2)
Factorization of p(x) = (x+3√2)(x-√2)
To get zeroes we write p(x) = 0
=> (x+3√2)(x-√2)=0
=> x+3√2 = 0 or x-√2= 0
=> x = -3√2 or x = √2
Zeroes are -3√2 and √2
f)
Given expresion is q(x) = √3x^2 + 10x + 7√3
=> q(x) =√3x²+10x+7√3
=> q(x) =√3x²+3x+7x+7√3
=> q(x) =√3x(x+√3)+7(x+√3)
=> q(x) = (x+√3)(√3x+7)
Factorization of q(x) = (x+√3)(√3x+7)
To get zeroes we write q(x) = 0
=> (x+√3)(√3x+7) = 0
=> x+√3 = 0 or √3x+7 = 0
=> x = -√3 or √3x = -7
=> x = -√3 or x = -7/√3
Zeroes are -√3 and -7/√3
g)
Given expresion is f(x) = x^2 − (√3 + 1)x + √3
=> f(x) = x²-√3x-x+√3
=> f(x) = x²-x-√3x+√3
=> f(x) = x(x-1)-√3(x-1)
=> f(x) = (x-1)(x-√3)
Factorization of f(x) = (x-1)(x-√3)
To get zeroes we write f(x) = 0
=> (x-1)(x-√3) = 0
=> x-1 = 0 or x-√3= 0
=> x = 1 or x = √3
Zeroes are 1 and √3
h)
Given expresion is g(x) = a(x^2 + 1) − x(a^2 + 1
=> g(x) = a(x² + 1) − x(a² + 1)
=> g(x) = ax²+a-a²x-x
=> g(x) = ax²-a²x-x+a
=> g(x)= ax(x-a)-1(x-a)
=> g(x) = (x-a)(ax-1)
Factorization of g(x) = (x-a)(ax-1)
To get zeroes we write g(x) = 0
=> (x-a)(ax-1) = 0
=>x-a = 0 or ax-1 = 0
=> x = a or ax = 1
=> x = 1 or x = 1/a
Zeroes are 1 and 1/a