Let p and q be the roots of the equation $x^{2} - 2 x + A = 0,$ and let r and s be the roots of the equation $x^{2} - 18 x + B = 0.$ If p < q < r < s are in arithmetic progression. The value of (A+B) equals

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Let r be a root of the equation x2+ 2x + 6 = 0. The value of (r + 2) (r + 3) (r + 4) (r + 5) is equal to.

The correct option is C -126 r be a root ⇒r2 + 2r + 6 = 0 ...................(1) now (r+2) (r+3) (r+4) (r+5) = (r2 + 5r +6) (r2+ 9r + 20) = (3r) (7r + 14) using (i) = 21 (r2+ 2r) = -126 using (i)

Let r be a root of the equation $x^{2}$ + 2x + 6 = 0. The value of (r + 2) (r + 3) (r + 4) (r + 5) is equal to.

The correct option is C
-126

r be a root $\Rightarrow r^{2}$ + 2r + 6 = 0 ...................(1)

now (r+2) (r+3) (r+4) (r+5)

= ( $r^{2}$ + 5r +6) ( $r^{2}$ + 9r + 20)

= (3r) (7r + 14) using (i)

= 21 ( $r^{2}$ + 2r)

= -126 using (i)