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If one zero of the polynomial ax2 + bx + c is positive and the other negative then (a,b,c εR, a = 0)
- a)a and b are of opposite signs
- b)a and c are of opposite signs
- c)b and c are of opposite signs
- d)a,b,c are all of the same sign
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If one zero of the polynomial ax2+ bx + c is positive and the other ne...
if α and β are two roots of equation ax2+bx+c=0
product of roots α*β = c/a
now if one root is negative and other positive, then product of the roots should be negative.
i.e c/a is negative which means both a and c are of opposite signs.
Most Upvoted Answer
If one zero of the polynomial ax2+ bx + c is positive and the other ne...
) must satisfy the following conditions:
1. The coefficient a must be nonzero, since otherwise the polynomial would reduce to a linear function with only one root.
2. The coefficients b and c must have opposite signs, since otherwise both roots would have the same sign.
3. The discriminant b^2 - 4ac must be positive, since otherwise both roots would be either real and equal or complex conjugates with the same real part.
Therefore, one possible set of values for (a, b, c) that satisfy these conditions is:
a = 1 (or any nonzero value)
b = -2
c = -1
This gives the polynomial x^2 - 2x - 1, which has roots approximately equal to -0.41 and 2.41.
1. The coefficient a must be nonzero, since otherwise the polynomial would reduce to a linear function with only one root.
2. The coefficients b and c must have opposite signs, since otherwise both roots would have the same sign.
3. The discriminant b^2 - 4ac must be positive, since otherwise both roots would be either real and equal or complex conjugates with the same real part.
Therefore, one possible set of values for (a, b, c) that satisfy these conditions is:
a = 1 (or any nonzero value)
b = -2
c = -1
This gives the polynomial x^2 - 2x - 1, which has roots approximately equal to -0.41 and 2.41.
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Community Answer
If one zero of the polynomial ax2+ bx + c is positive and the other ne...
Since one root is positive and the other is negative their product is always negative
The product of roots = c/a
For c/a to be negative either of c or a must be negative but both should not be negative. Therefore a and c must be of opposite signs.
The product of roots = c/a
For c/a to be negative either of c or a must be negative but both should not be negative. Therefore a and c must be of opposite signs.
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