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if $3x^2+2ax+b+5\sin 2x >0$, then prove/disprove that $a^2-3b+15<0$.($x\in \mathbb R$)

If disproven find correct inequality relating $a,b$

I don't know where to start. Any hint will be appreciated

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In the best case $$3x^2+2ax+b+5>0$$ Thus, the quadratic form does not change in sign and has no root $$\Delta<0$$

$$(2a)^2-4(3)(b+5)<0$$

divided by 4

$$a^2-(3)(b+5)<0$$

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