If the line y = x touches the parabola y = x2 + bx + c at the point (

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
Answer» 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

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

Answer»

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

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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

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