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 + .
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Answer:
Given that the zeros of the quadratic polynomial ax
Given that the zeros of the quadratic polynomial ax2
Given that the zeros of the quadratic polynomial ax2+bx+c,c
Given 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.=>b
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
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
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=>b
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
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=4ac
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 b
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 b2
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.
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.