Question

is a-b, a and a + b are zeros of the polynomial f (x )is equal to 2 x ^3 -6x^2 + 5 x- 7 find the value of a

Answer 1

In general Sum of zeroes of a cubic polynomial is -b/a , If the cubic polynomial is ax³+bx²+cx+d,

According to your question the zeros of polynomial are a-b, a  and b Sum of them is a-b+a+b = 3a, and also the sum of the zeros is -(-6)/2 = 3,

Now 3a = 3, => a = 1,
Similarly if a,b,c are the roots of cubic polynomial, Then , ab+bc+ca = c/a,
Here a²-ab + a² + ab + a² - b² = 5/2,
=> 3a² -b² = 5/2,
=> 3-5/2 = b²
=> 1/2 = b²
b = + or - (1/√2),
b can be either of those, But the roots will always be 1, (1-(1/√2)), (1+1/√2)), as if keep +b there will be - in one root, if keep -b there will + in one root,

Hope you understand, Have a great day !

Answer 2

Hello salena !

◆ sum of roots

we know that sum of roots of cubic polynomial is ( - coeff. of x^2) / coeff. of x^3)

let polynomial be f(x)

=) f(x) = 2x^3 -6x^2 +5x - 7

sum of roots = -(-6/2 )= 3

=) (a-b)+ a + (a+b) = 3

=) 3a = 3

=) a = 1

so value of a = 1

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