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Question Number 175943 by CrispyXYZ last updated on 10/Sep/22

(1) ∃x∈R, x^2 +x+a=0. find the range of a. (2) ∀x∈R, x^2 +x+a=0. find the range of a.

(1)∃x∈R,x2+x+a=0.findtherangeofa.(2)∀x∈R,x2+x+a=0.findtherangeofa.

Answered by mahdipoor last updated on 10/Sep/22

1) x=((−1±(√(1−4a)))/2) ⇒ 1−4a≥0 ⇒ a≤(1/4) 2)for example : get x_1 =1 and x_0 =0 (x_1 )^2 +x_1 +a=(x_0 )^2 +x_0 +a=0 2+a=a=0 ⇒ ∄a∈R

1)x=−1±1−4a2⇒1−4a⩾0⇒a⩽142)forexample:getx1=1andx0=0(x1)2+x1+a=(x0)2+x0+a=02+a=a=0⇒∄a∈R

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