Find the smallest value of -8 p -7 for which - x 2-5 x -7- p -6- x 2-5 x -1- p - for all x -1-3-

We must have (x^2 5x+1 p)≥ 0 ∀ x ϵ [ 1,3] ⇒ (x^2 5x+1 p)≥ 0 ∀ x ϵ [ 1,3] upward parabola with vertex (x=5/2,y= p 21/4 ) ∴ p 21/4≥ 0 ⇒ p+21/4≤ 0 ⇒ p ≤ 21/4 ∴ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Section Formula

Find the smal...

Question

Find the smallest value of $(\frac{- 8 p}{7})$ for which $| x^{2} - 5 x + 7 - p | = 6 + | x^{2} - 5 x + 1 - p |$ for all $x ϵ [- 1, 3]$ . ___

Open in App

Solution

We must have
$(x^{2} - 5 x + 1 - p) \geq 0 \forall x ϵ [- 1, 3] \Rightarrow (x^{2} - 5 x + 1 - p) \geq 0 \forall x ϵ [- 1, 3] u p w a r d p a r a b o l a w i t h v e r t e x (x = \frac{5}{2}, y = - p - \frac{21}{4}) ∴ - p - \frac{21}{4} \geq 0 \Rightarrow p + \frac{21}{4} \leq 0 \Rightarrow p \leq - \frac{21}{4} ∴ p ϵ (- \infty, \frac{21}{4})$
Smallest value of $(\frac{- 8 p}{7}) = \frac{- 8 p}{7} = \frac{- 8}{7} \times - \frac{21}{4} = 6$

Suggest Corrections

Similar questions

Q. The smallest value of

(\frac{- 8 p}{7})

for which

∣ ∣ x^{2} - 5 x + 7 - p ∣ ∣ = 6 + ∣ ∣ x^{2} - 5 x + 1 - p ∣ ∣

for all

x \in [- 1, 3]

Q. Find the values of

x

for which

x^{2} + 6 < 5 x

Q. If

p (x) = x^{2} - 5 x - 6,

then find the values of

p (1), p (2), p (3), p (0), p (- 1), p (- 2), p (- 3)

Q. All the values of

x

for which

x^{2} - 5 x + 6

is non-negative are

Q. The integral

\int \frac{e^{3 {log}_{e} 2 x} + 5 e^{2 {log}_{e} 2 x}}{e^{4 {log}_{e} x} + 5 e^{3 {log}_{e} x} - 7 e^{2 {log}_{e} x}} d x, x > 0,

is equal to :
(where c is a constant of integration)

Join BYJU'S Learning Program

Find the smallest value of (−8p7) for which |x2−5x+7−p|=6+|x2−5x+1−p| for all xϵ[−1,3]. ___

We must have (x2−5x+1−p)≥0∀xϵ[−1,3]⇒(x2−5x+1−p)≥0∀xϵ[−1,3]upwardparabolawithvertex(x=52,y=−p−214)∴−p−214≥0⇒p+214≤0⇒p≤−214∴pϵ(−∞,214) Smallest value of (−8p7)=−8p7=−87×−214=6

Find the smallest value of $(\frac{- 8 p}{7})$ for which $| x^{2} - 5 x + 7 - p | = 6 + | x^{2} - 5 x + 1 - p |$ for all $x ϵ [- 1, 3]$ . ___