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The expression x2 + kx + 9 becomes positive for what values of k (given that x is real)?
- a)k < 6
- b)k > 6
- c)|K|<6
- d)|k|< 6
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The expression x2 + kx + 9 becomes positive for what values of k (give...
Method to Solve :
If the roots are equal(double root) it means that discriminant of quadratic equation b^2-4ac=0
general form of quadratic equation is ax^2+bx+c=0
in this case a=1 b=k and c=9
b^2-4ac=0 then:
k^2-36=0
(k-6)(k+6)=0
k=6 or k=-6
For k=6 or k= -6 given equation has real and equal roots
general form of quadratic equation is ax^2+bx+c=0
in this case a=1 b=k and c=9
b^2-4ac=0 then:
k^2-36=0
(k-6)(k+6)=0
k=6 or k=-6
For k=6 or k= -6 given equation has real and equal roots
Most Upvoted Answer
The expression x2 + kx + 9 becomes positive for what values of k (give...
For the expression to be positive, the quadratic equation x^2 + kx + 9 = 0 must have no real roots (since the sign of the expression changes when x crosses the root). This happens when the discriminant is negative:
b^2 - 4ac < />
(k^2 - 4*1*9) < />
k^2 < />
-6 < k="" />< />
Therefore, the expression x^2 + kx + 9 becomes positive for all values of k between -6 and 6 (excluding 0, which would make the expression equal to 9 for all values of x).
b^2 - 4ac < />
(k^2 - 4*1*9) < />
k^2 < />
-6 < k="" />< />
Therefore, the expression x^2 + kx + 9 becomes positive for all values of k between -6 and 6 (excluding 0, which would make the expression equal to 9 for all values of x).
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Community Answer
The expression x2 + kx + 9 becomes positive for what values of k (give...
The roots should be imaginary for the expression to be positive i.e.
k2 - 36 < 0
thus - 6 < k < 6 or |k| < 6.
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