Question

Find the zeroes of the quadratic polynomial 3x^2 ‒10 x + 7 and verify the relationship between the zeroes and coefficients​

Answer 1

Answer:

q(x) = √3x2 + 10x + 7√3

We put q(x) = 0

⇒ √3x2 + 10x + 7√3 = 0

⇒ √3x2 + 3x + 7x + 7√3x = 0

⇒ √3x(x + √3) + 7 (x + √3) = 0

⇒ (x + √3)(√3x + 7) = 0

This gives us 2 zeros, for x = -√3 and x = -7/√3

Hence, the zeros of the quadratic equation are -√3 and -7/√3.

Now, for verification

Sum of zeros = – coefficient of

x /coefficient of x2 -√3 + (-7/√3)

= – (10) /√3 (-3-7)/ √3

= -10/√3 -10/ √3

= -10/√3

Product of roots =

constant /coefficient of x2 (-√3) x (-7/√3)

= (7√3)/√3 7 = 7

Therefore, the relationship between zeros and their coefficients is verified.