If the line y = x touches the parabola y = x2 + bx + c at the point (1, 1), then
(A) b = 0, c = −1
(B) b = −1, c = Z
(C) b = −1, c = −1
(D) b = −1, c = 1
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If the line y = x touches the parabola y = x2 + bx + c at the point (1, 1), then
(A) b = 0, c = −1
(B) b = −1, c = Z
(C) b = −1, c = −1
(D) b = −1, c = 1
If the line y = x touches the parabola y = x2 + bx + c at the point (1, 1), then
(A) b = 0, c = −1
(B) b = −1, c = Z
(C) b = −1, c = −1
(D) b = −1, c = 1
Correct option (D) b = −1, c = 1
Explanation :
The point (1, 1) lies on the parabola, which implies that
b + c = 0 …(1)
Also, y = x touches the parabola
⇒ the quadratic x2 + (b – 1) x + c = 0 has equal roots
⇒ (b – 1)2 – 4c = 0
Therefore, from Eq. (4.108), we get
(b – 1)2 + 4b = 0
⇒(b + 1)2 = 0
⇒b = -1 and c = 1