If x^2-3 ax+14=0 and x^2+2 ax-16=0 have a common root, then a^4+a^2.

Question

Accepted Answer

Correct answer: B. (b) Given that, x^2-3 ax+14=0 and x^2+2 ax-16=0 have a common root. Let the common roots is . Then, ^2-3 aα+14=0 and ^2+2 aα-16=0 by cross multiplication method ^248a-28a= 14+16= 12a+3a ⇒ ^220a= 30= 15a So, ^220a= 30 and 130= 15a ⇒ = 20a30 and = 305a ⇒ = 23a and = 6a So , 2a3= 6a ⇒2a^2=18 ⇒a^2=9 ⇒a= 3 Now ,a^4+a^2= ( 3 )^4+ ( 3 )^2=81+9=90

$If x^{2} - 3 ax + 14 = 0 and x^{2} + 2 ax - 16 = 0 have a common root, then a^{4} + a^{2} .$

Solution

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