The values of p and q if x-1 is a common factor of f(x)=x⁴-px³ +7qx+1, and g(x)=x²-4x² + px² +qx-3,are 13/2 and -1/2 respectively.
What is a factor?
In Mathematics, factors are positive integers that can divide a number evenly. Suppose we multiply two numbers to get product. The number that is multiplied are the factors of the product. Each number is factor of itself. Factors have many real-life examples, such as arranging sweets in box, arranging numbers in pattern, distributing chocolates among children, etc. To find the factors of number, we need to use the multiplication or division method.
Factors are numbers that can divide a number exactly. Hence, after the division, there is no remainder left. Factors are numbers you multiply together to get the another number. Thus, factor is the divisor of another number.
f(x)=[tex]x^{4}-px^{3}+7qx+1[/tex]
= 1-p+7q+1
= p-7q=2---------1
g(x)= [tex]-3x^{2} +px^{2} +qx-3[/tex]
= -3+p+q-3
=p+q= 6----------2
p-7q=2
p+q=6
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By subtracting 2 from 1
-8q=4
q=-1/2
putting value of q in equation 2 we get,
p+(-1/2)=6
p=6+[tex]\frac{1}{2}[/tex]
p=13/2
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