x 2 - 34 x + c = 0 In the given equation, c is a constant. The equation has

Question

x 2 - 34 x + c = 0 In the given equation, c is a constant. The equation has no real solutions if c &#62; n . What is the least possible value of n ?

Accepted Answer

The correct answer is 289 . A quadratic equation of the form a x 2 + b x + c = 0 , where a , b , and c are constants, has no real solutions when the value of the discriminant, b 2 - 4 a c , is less than 0 . In the given equation, x 2 - 34 x + c = 0 , a = 1 and b = - 34 . Therefore, the discriminant of the given equation can be expressed as - 34 2 - 4 1 c , or 1,156 - 4 c . It follows that the given equation has no real solutions when 1,156 - 4 c < 0 . Adding 4 c to both sides of this inequality yields 1,156 < 4 c . Dividing both sides of this inequality by 4 yields 289 < c , or c > 289 . It's given that the equation x 2 - 34 x + c = 0 has no real solutions when c > n . Therefore, the least possible value of n is 289 .

Question x-2-34