If the range of fx-x2-7x-60 in x- -3-2- is -m- n- then the value of m-n is

Given polynomial nbsp; f(x)= x^2+7x+60 x coordinate of the vertex nbsp; b2a = nbsp; 7 2= 7 2 We know that nbsp; 72 2⇒ b2a 2 Now, ploting the graph ...

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

Byju's Answer

Standard XII

Mathematics

Range of Quadratic Expression

If the range ...

Question

If the range of $f (x) = - x^{2} + 7 x + 60$ in $x \in [- 3, 2]$ is $[m, n]$ , then the value of $m + n$ is

Open in App

Solution

Given polynomial
$f (x) = - x^{2} + 7 x + 60$
$x -$ coordinate of the vertex
$- \frac{b}{2 a} = - \frac{7}{- 2} = \frac{7}{2}$
We know that
$\frac{7}{2} > 2 \Rightarrow - \frac{b}{2 a} > 2$

Now, ploting the graph of the polynomial, we get

Now,
$f (- 3) = - 9 - 21 + 60 = 30 f (2) = - 4 + 14 + 60 = 70$
Therefore, the range of the polynomial is
$[30, 70] ∴ m + n = 100$

Suggest Corrections

Similar questions

Q. If the range of

f (x) = - x^{2} + 7 x + 60

x \in [- 3, 2]

[m, n]

, then the value of

m + n

Q. The range of

f (x) = - x^{2} + 7 x + 60

x \in [- 3, 2]

Q. The range of

f (x) = - x^{2} + 7 x + 60

x \in [- 3, 2]

f : R \to R,

f (x) = \frac{3 x^{2} + m x + n}{x^{2} + 1} .

If the range of

f (x)

[- 4, 3],

then

Q. If the range of

f (x) = x^{2} + 5 x - 2

(- \frac{m}{4}, \infty)

then the value of

m

is equal to

Join BYJU'S Learning Program

If the range of f(x)=−x2+7x+60 in x∈[−3,2] is [m,n], then the value of m+n is

Given polynomial f(x)=−x2+7x+60 x− coordinate of the vertex −b2a=−7−2=72 We know that 72>2⇒−b2a>2 Now, ploting the graph of the polynomial, we get Now, f(−3)=−9−21+60=30f(2)=−4+14+60=70 Therefore, the range of the polynomial is [30,70]∴m+n=100

If the range of $f (x) = - x^{2} + 7 x + 60$ in $x \in [- 3, 2]$ is $[m, n]$ , then the value of $m + n$ is