If {x^2} + 2ax + 10 - 3a 0 for all x in R,t | vedclass

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Question

(A) For a quadratic expression $Ax^2 + Bx + C > 0$ to be true for all $x \in R$,the discriminant $D$ must be less than $0$ and $A > 0$.Here,$A = 1$,wh

Vedclass · Accepted Answer

$-5 < a < 2$

Vedclass · Answer

(A) For a quadratic expression $Ax^2 + Bx + C > 0$ to be true for all $x \in R$,the discriminant $D$ must be less than $0$ and $A > 0$.Here,$A = 1$,which is $> 0$.The discriminant $D = B^2 - 4AC = (2a)^2 - 4(1)(10 - 3a) $4a^2 - 40 + 12a Dividing by $4$,we get $a^2 + 3a - 10 Factoring the quadratic,we get $(a + 5)(a - 2) This inequality holds when $a$ lies between the roots,so $-5 < a < 2$.

If ${x^2} + 2ax + 10 - 3a > 0$ for all $x \in R$,then

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