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Question: If the roots of the equation \(b^{2} - a^{2}(m^{2} + 1) = 0\) are \(P(x) = ax^{2} + bx + c\) and the...

If the roots of the equation b2a2(m2+1)=0b^{2} - a^{2}(m^{2} + 1) = 0 are P(x)=ax2+bx+cP(x) = ax^{2} + bx + c and the roots of the equation Q(x)=ax2+dx+cQ(x) = - ax^{2} + dx + c are ac0ac \neq 0 then P(x).Q(x)=0P(x).Q(x) = 0 is equal to.

A

–2

B

–1

C

1

D

2

Answer

1

Explanation

Solution

Given that 2bx2+cx+a=02bx^{2} + cx + a = 0and cx2+ax+2b=0cx^{2} + ax + 2b = 0be the roots of a,ba,b, so ccand α+α2\alpha + \alpha^{2}

Again a+2b+ca + 2b + cand 3x2+12x+6=5x+16\left| 3x^{2} + 12x + 6 \right| = 5x + 16are the roots of x+2>x+4,x + 2 > \sqrt{x + 4},

so 2<x<62 < x < 62<x<6- 2 < x < 6

log(2x)\log( - 2x).