Question

find the zeroes of x2-7x+10 and find the relation between the zeroes and coefficients​

Answer 1

Note:

1) To find the zeros of a polynomial, equate it to zero.

2) If we consider a quadratic polynomial in variable x , say ; ax^2 + bx + c

Then,

a) Sum of zeros is given by ;

(-coefficiennt of x)/(coefficient of x^2)

ie; -b/a

b) Product of zeros is given by ;

zeros is given by ;(constant term)/(coefficient of x^2)

)/(coefficient of x^2)ie; c/a.

Here,

The given quadratic polynomial is;

x^2 - 7x + 10.

To find the zeros of the given quadratic polynomial , equate it to zero;

ie;

=> x^2 - 7x + 10 = 0

=> x^2 - 2x - 5x + 10 = 0

=> x(x - 2) - 5(x - 2) = 0

=> (x - 2)(x - 5) = 0

=> (x - 2) = 0 OR (x - 5) = 0

=> x = 2 OR x = 5

Now,

Sum of zeros

= 2 + 5

= 7

= - (-7/1)

= (-coefficiennt of x)/(coefficient of x^2)

Product of zeros

= 2•5

= 10

= 10/1

= (constant term)/(coefficient of x^2)

Hence verified.