When Aryan was watching a boy playing football, he visualised that the path traced by the ball resembles a parabola, which can be represented by the quadratic polynomial 2+ b + c, a ≠0. He further noted that a quadratic polynomial has atmost two real zeroes. If and are the zeroes of 2− b + c, a ≠0 then calculate + .

When Aryan was watching a boy playing football, he visualised that the

1.	When Aryan was watching a boy playing football, he visualised that the path traced by the ball resembles a parabola, which can be represented by the quadratic polynomial 2+ b + c, a ≠0. He further noted that a quadratic polynomial has atmost two real zeroes. If and are the zeroes of 2− b + c, a ≠0 then calculate + .
Answer» Given that the ZEROS of the quadratic polynomial axGiven that the zeros of the quadratic polynomial ax2Given that the zeros of the quadratic polynomial ax2+bx+C,cGiven that the zeros of the quadratic polynomial ax2+bx+c,cGiven that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.Given that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the DISCRIMINANT(D) has to be zero.Given that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the discriminant(D) has to be zero.=>bGiven that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the discriminant(D) has to be zero.=>b2Given that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the discriminant(D) has to be zero.=>b2−4ac=0Given that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the discriminant(D) has to be zero.=>b2−4ac=0=>bGiven that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the discriminant(D) has to be zero.=>b2−4ac=0=>b2Given that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the discriminant(D) has to be zero.=>b2−4ac=0=>b2=4acGiven that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the discriminant(D) has to be zero.=>b2−4ac=0=>b2=4acSince. L.H.S bGiven that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the discriminant(D) has to be zero.=>b2−4ac=0=>b2=4acSince. L.H.S b2Given that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the discriminant(D) has to be zero.=>b2−4ac=0=>b2=4acSince. L.H.S b2cannot be NEGATIVE, THUS, R.H.S. can also be never negative.Given that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.=> Value of the discriminant(D) has to be zero.=>b2−4ac=0=>b2=4acSince. L.H.S b2cannot be negative, thus, R.H.S. can also be never negative.Therefore, a and c must be of the same sign.

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