Stockholders of Solarex Corp. yesterday approved a $12 million takeover of the pioneering solar-energy company by Standard Oil Co. of Indiana (Amoco).

But objections from minority shareholders could stall completion of the deal, perhaps endangering financially strapped Solarex. An Amoco official said the closely held Rockville company's finances are in "a very critical state" and indicated that the company, in which Amoco already holds a 38 percent stake, could face severe cash-flow problems within a few days.

"They've been right on the ragged edge for some period of time," said Gordon McKeague, Amoco's general manager for corporate development and a member of Solarex's board. "They need money." Solarex lost nearly $9.8 million last year on sales of $18.2 million, and sources say the losses have continued as expected markets for the company's photovoltaic cells, which turn sunlight into electricity, have failed to materialize.

Amoco had been hoping to complete the takeover of Solarex and its subsidiary, Semix, which makes raw silicon used in the production of solar cells, today.

But the merger could be scuttled or delayed by the objections of a group of Semix shareholders that Amoco's offering price of $15 per share of Semix stock is too low. Amoco has conditioned its acquisition of Solarex on an ability to complete the takeover of Semix, too.

The objections were raised at a meeting yesterday called to win the approval of Semix shareholders for the merger. Solarex owns approximately 54 percent of Semix's 717,000 common shares, and Amoco holds another 24 percent, and as a result, the merger passed easily. Solarex shareholders, voting later in the day, also easily approved the merger with Amoco, over the objections of some minority shareholders about the $2.50-a-share offering price for Solarex.

The dissenting Semix holders, a group of European banks and investors who said they represented 12 percent of the company's stock, said they would attempt to force Amoco to raise its price for Semix through the appraisal-rights procedure of corporation law in Delaware, where Semix is incorporated. Under that rule, the dissenting shareholders can ask Delaware courts to appraise the value of Semix stock. If the courts find Semix is worth more than Amoco wants to pay, the Chicago-based oil company could then be forced to pay the dissenting shareholders more for their shares.

"We're confronted with a fait accompli--$15," said Jost V. Steinbruchel, first vice president of Credit Suisse, a large Swiss bank that represented several shareholders at the meeting. "There's no doubt that we'll be able to demonstrate that what's happening . . . is that Standard is landing a financial coup at the expense of the Semix shareholders."

Under its merger agreement with Semix, Amoco may terminate its bid for Semix if holders of more than 10 percent of Semix's shares exercise their appraisal rights. That condition was apparently met yesterday by the dissenters. But Amoco could waive the condition, take its chances with the Delaware courts' appraisal of Semix's value, and complete the takeover of Semix and Solarex.

The deal cannot be completed until Amoco decides what to do about the appraisal rights condition, and McKeague said yesterday that the big oil company was studying the situation.

But John Corsi, Solarex's president, said last evening, "It's my belief that they will waive" and the merger will be completed as scheduled.

The dissenting shareholders are basing their request for more money for their stock on prices paid previously by Amoco for Semix stock. Amoco paid $80 a share for Semix stock purchased in October 1980 and $96 a share in June 1982, according to the shareholders. In March, however, Solarex secured an emergency $7.3 million loan from Amoco with 170,000 shares of Semix stock, or about $43 a share. And Amoco purchased 5,000 shares of Semix stock in August for $15 each.

Amoco officials say the price of the stock has declined as the financial condition of Semix and Solarex has worsened, and say the $15 offering price is fair.