Multiple choice

It is given that expression $a x ^ { 2 } + b x + c$ take negatives values for all $x < 7$.Then

  1. The equation $a x ^ { 2 } + b x + c = 0$,has equal roots

  2. a is negative:

  3. a and b is both negative:

  4. none of the foregoing statements correct'
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If a quadratic ax^2 + bx + c is negative for all x < 7, the parabola must open downwards (a < 0) and the root must be at x = 7. If it were positive for x < 7, a would be positive.

AI explanation

If the expression ax^2 + bx + c takes negative values for all x < 7, then a linear function like a = -1, b = 0, c = -1 will satisfy the condition. However, a quadratic expression that is negative for all real x must have a negative leading coefficient. A linear function or a quadratic opening downwards satisfies the condition that the leading coefficient a is negative.

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