If | beginmatrix x2+x 3x-1 -x+3 2x+1 2+x2 x3-3 x-3 x2+4 3x endmatrix | =a0+a1x+a2x2+.....+a7x7, then the value of a0 is

Question

If | beginmatrix x2+x 3x-1 -x+3 2x+1 2+x2 x3-3 x-3 x2+4 3x endmatrix | =a0+a1x+a2x2+.....+a7x7, then the value of a0 is (A) 25 (B) 24 (C) 23 (D) 22

Tardigrade Admin · Accepted Answer

We have | beginmatrix x2+x 3x-1 -x+3 2x+1 2+x2 x3-3 x-3 x2+4 3x endmatrix | =x2+x[(2+x2)(3x)-(x2+4)(x3-3)] -(3x-1)[(2x+1)3x-(x-3)(x3-3)] +(-x+3)[(2x+1)(x2+4) -(x-3)(2+x2) =21+35x+12x2-7x3-9x4 +2x5-x6-x7 ⇒ a0=21

Q. If ∣∣​x2+x2x+1x−3​3x−12+x2x2+4​−x+3x3−33x​∣∣​ =a0​+a1​x+a2​x2+.....+a7​x7, then the value of a0​ is

25

24

23

22

21

We have ∣∣​x2+x2x+1x−3​3x−12+x2x2+4​−x+3x3−33x​∣∣​ =x2+x[(2+x2)(3x)−(x2+4)(x3−3)] −(3x−1)[(2x+1)3x−(x−3)(x3−3)] +(−x+3)[(2x+1)(x2+4) −(x−3)(2+x2) =21+35x+12x2−7x3−9x4 +2x5−x6−x7 ⇒ a0​=21

Q. If $∣ ∣ x^{2} + x 2 x + 1 x - 3 3 x - 1 2 + x^{2} x^{2} + 4 - x + 3 x^{3} - 3 3 x ∣ ∣$ $= a_{0} + a_{1} x + a_{2} x^{2} + ..... + a_{7} x^{7},$ then the value of $a_{0}$ is